BRICSNewsletterBasic Research in Computer Science No 6, April 1997

In this Issue

Welcome 1

Coming Events 2Algebraic Theory of Automata, Temporal

Logic and Expressiveness . . . . . . . . 2Information Theoretic Security in Cryp-

tography . . . . . . . . . . . . . . . . . . 2Combinatorial Optimisation Meeting . . . 2First Order Logic with Dependent Sorts,

Simulation, and Higher Dim. Categories 2Inductive Logic Programming . . . . . . . 2Combinatorial Pattern Matching ’97 . . . . 3Computer Science Logic ’97 . . . . . . . . 3School on Comp. and Syntactic Methods . 4School on Natural Computation . . . . . . 4

Reports on Events 4

Newly Appointed Researchers and Guests 8

Dissertation Abstracts 10Worst Case Efficient Data Structures . . . 10Trust and Dependence Analysis . . . . . . 11An Axiomatic Approach to Adequacy . . 13

New Reports 14

Notes Series 17

Lecture Series 18

Dissertations Series 22

News 22BRICS International PhD School . . . . . . 22Tools for Automated Verification of

Embedded Software . . . . . . . . . . . 22

Calendar of Events 24

BRICS Address and World Wide Web 24

Welcome

Welcome to the sixth issue of the BRICS newslet-ter. Its purpose is to inform you of appointments,publications, courses and other activities withinBRICS. Further details can be obtained by con-tacting the addresses on the back page.

We are later than we intended in issuing thisBRICS newsletter. Christmas and the early newyear were occupied both with LICS’97 (GlynnWinskel is program chair this year) and with pro-ducing a report on the first three years of BRICS;the report is to serve both as a progress sum-mary and an application to the Danish NationalResearch Foundation for BRICS to be funded foranother five years after ’98.

This year marks the start of an important ven-ture, the BRICS International PhD School, un-der the direction of Mogens Nielsen. The school,like BRICS funded by the Danish National Re-search Foundation, is an experiment in Dan-ish postgraduate education, the idea being tosupplement the twenty or so Danish PhD stu-dents of BRICS with a corresponding numberfrom abroad. Yearly there are around five stu-dentships for students from abroad. While thestudents’ core education will be based on theBRICS areas of semantics, logic and algorith-mics, the PhD School is also concerned with pro-viding the back-up for students interested in ap-plying their theoretical knowledge to more ap-plied areas.

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Coming Events

For details see the BRICS Activities web page:

www.brics.dk/Activities.

Algebraic Theory of Automata, Tempo-ral Logic and Expressiveness

April 29 and 30, 1997, Denis Therien, School ofComputer Science, McGill University, Canada,will give two double lectures covering the fol-lowing topics: algebraic theory of automata,decomposition of finite semigroups, logical de-scription of ∗-free languages and regular lan-guages and boolean circuits.

Information Theoretic Security inCryptography

May 1–2, 1997, Ueli Maurer, Department of Com-puter Science, ETH (The Swiss Federal Instituteof Technology), Zurich, Switzerland, will give amini-course on Information Theoretic Security inCryptography.

Cryptography is sometimes perceived as beinginherently based on unproven computational as-sumptions. While this has never been really true,the last few years of research have demonstratedin a rather dramatic way that many types of datasecurity can be realized—also in practice—basedon no assumptions whatsoever.

One example of this is Quantum Cryptography,where security is based on fundamental laws ofquantum physics. Both the physical realizationand the theoretic background has strong links tothe related field of Quantum Computing. An-other example is noisy communication. Whilenoise is usually dealt with as a problem thatshould be removed, it can also be turned into anadvantage allowing secure communication, as-suming only that enemies cannot totally removenoise from the data they receive.

Information theory and related topics, such as

universal hashing, are at the heart of such “un-conditional” cryptography. The course will in-troduce the necessary theory and show a num-ber of scenarios where the theory applies.

Combinatorial Optimisation Meeting

May 5–6, 1997, BRICS is organising a meeting oncombinatorial optimisation. The aim is to bringtogether Danish (and non-Danish) combinatorialoptimisation people and discuss current state ofthe art and research directions. Algorithmic as-pects are of particular interest.

The featured speaker of the meeting is MartinGrotschel from the Konrad-Zuse-Zentrum furInformationstechnik, Berlin (ZIB). A number ofother people have accepted our invitation to talkat the meeting. Further information is availableat www.brics.dk/Activities/97/CombOpt.

First Order Logic with DependentSorts, Simulation, and Higher Dimen-sional Categories

In the middle of May, Michael Makkai, McGillUniversity, Canada, will give a mini-course onfirst order logic with dependent sorts, simula-tion, and higher dimensional categories.

Inductive Logic Programming

May 20–23, 1997, Nada Lavrac, Department of In-telligent Systems, Jozef Stefan Institute, Ljubl-jana, Slovenija, and Peter Flach, Infolab, De-partment of Management Information Science,Tilburg University, Holland, will give three dou-ble lectures on Inductive Logic Programming.

Inductive logic programming (ILP) is a researcharea, combining principles of inductive machinelearning and logic programming. ILP aims at a

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formal framework and practical algorithms forinductively learning relational descriptions inthe form of logic programs. ILP is of interestto inductive machine learning as it significantlyextends the usual attribute-value representationand consequently enlarges the scope of machinelearning applications; it is also of interest to logicprogramming as it extends the basically deduc-tive framework of logic programming towardsthe use of induction. The course aims at givingan overview of the field, with an emphasis on thefoundations and basic techniques.

ILP has already shown its potential for appli-cations. Applications in a machine learningcontext include: knowledge acquisition, induc-tive data engineering, scientific discovery andknowledge discovery in databases. Potential ap-plications in logic programming include: knowl-edge base updating, logic program synthesis, de-bugging and verification of programs, and deriv-ing integrity constraints from databases.

Combinatorial Pattern Matching ’97

The 8th Annual Symposium on CombinatorialPattern Matching (CPM ’97) will be held at theComputer Science Department in the Universityof Aarhus, Arhus, Denmark, from Monday, June30, through Wednesday, July 2, 1997.

Combinatorial Pattern Matching addresses is-sues of searching and matching strings and morecomplicated patterns such as trees, regular ex-pressions, graphs, point sets, and arrays. Thegoal is to derive non-trivial combinatorial prop-erties for such structures and then to exploitthese properties in order to achieve improvedperformance for the corresponding computa-tional problem.

In recent years, a steady flow of high-quality re-search on this subject has changed a sparse set ofisolated results into a full-fledged area of algo-rithmics with important applications. This areais expected to grow even further due to the in-creasing demand for speed and efficiency that

comes from molecular biology, but also from ar-eas such as information retrieval, pattern recog-nition, compiling, data compression, programanalysis and security. The objective of annualCPM gatherings is to provide an international fo-rum for research in combinatorial pattern match-ing.

In connection with the symposium on June 28and June 29, a summer school will be organisedat the same location and focus on topics mainlywithin computational biology.

The event is organised Jotun Hein, Departmentof Ecology and Genetics, Institute of BiologicalSciences, University of Aarhus in cooperationwith Christian N. S. Pedersen, BRICS, Aarhus.

Please see www.brics.dk/CPM97 for further in-formation.

Computer Science Logic ’97

The Annual Conference of the European Associ-ation for Computer Science Logic (CSL ’97) willbe held in Aarhus in the period August 23–29,1997.

The conference is intended for computer scien-tists whose research activities involve logic, aswell as for logicians working on topics signifi-cant for computer science.

Scientific Program

August 23–24: Tutorials on Games and LogicS. Abramsky (Edinburgh): Game SemanticsE. A. Emerson (Austin): Games, µ-calculus, andprogram verificationW. Thomas (Kiel), I. Walukiewicz (Warsaw): De-terminacy, the Rabin Tree Theorem and its exten-sions

August 25–29: Invited Lectures and Con-tributed PapersInvited speakers: S. Buss (San Diego), H. Comon(Paris), T. Coquand (Gothenburg), M. Hyland(Cambridge), N. Immerman (Amherst), N. Klar-

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lund (Murray Hill), Y. Moschovakis (Los Ange-les), L. Pacholski (Wroclaw).

Student Grants

A limited number of grants to attend the Confer-ence and the Tutorials are available for students.The grants will cover local expenses and confer-ence fee, but will not cover travel expenses.

Further information can be obtained fromwww.brics.dk/CSL97.

School on Computational and Syntac-tic Methods

August 11–22, 1997, European Educational Fo-rum (see page 7) organises a School on Com-putational and Syntactic Methods in Mierlo, TheNetherlands.

The program of the school covers the followingtopics: Term Rewriting, Type Systems, Modelsof Concurrency, Effective Algebras and ProcessAlgebra.

Further information can be obtained by follow-ing the corresponding link on the EEF homepage: www.tucs.abo.fi/EEF.

School on Natural Computation

August 25–29, 1997, the European EducationalForum organises a School on Natural Computation,SNAC, at the Mauno Koivisto Centre, Turku,Finland.

The School on Natural Computation will con-centrate on four branches of natural computa-tion, namely artificial neural networks, geneticalgorithms, DNA-computing and quantum com-puting.

The main goal of the school is to establish a deepunderstanding of the theory and practice of nat-ural computation such that the participants areable to explore the paradigm and to assess its re-lation to other fields in order to specify better so-lutions to real world complex problems.

For further information, please consult the asso-ciated page: www.abo.fi/˜kaisa/SNAC.html.

Reports on Events

Set Constraints

On August 14 and 15, 1996, Dexter Kozen, JosephNewton Pew, Professor of Computer Science,Cornell University, Ithaca, NY, USA, gave acourse of six lectures on Set Constraints. Coursedescription and a list of references can be foundon the web.

Competitive Online Algorithms

During August 27–29, 1996, Susanne Albers, Max-Planck-Institut fur Informatik, Saarbrucken,Germany gave a mini-course on CompetitiveOnline Algorithms.

For the course notes, please see [LS-96-2] in theLecture Series below. Notes as well as slides areobtainable from www.brics.dk/LS/96/2.

Non-Interleaving Transition Systems

On October 3 and 4, 1996, Vladimiro Sassone,Dipartimento di Informatica, Pisa, Italy, gave amini-course on Non-Interleaving Transition Sys-tems. Course description is on the web.

Explicit Substitution

On October 10 and 11, in connection with theAutumn School on Verification, Kristoffer Høgsbro

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Rose, BRICS, gave a three lecture mini-course on“Explicit Substitution.”

The lecture notes appear as [LS-96-3] in theBRICS Lecture Series below. These notes andselected slides are available from the URL:www.brics.dk/LS/96/3.

Autumn School on Verification

October 28 – November 1, 1996.

We bring here a report written by on of theparticipants Robert-C. Riemann, LRI (Laboratoirede Recherche en Informatique), Universite Paris-Sud, Orsay, France, for the EATCS Bulletin (ap-peared in the February issue).

This years 5 day autumn school of the Basic Re-search In Computer Science (BRICS) institute washeld at the University of Aarhus, Denmark. Theevent centred on verification methods and toolsin theorem proving and model checking, andperspectives to combine both methods. 87 par-ticipants from 16 countries and 4 continents wereinvited by BRICS to attend the school. Every par-ticipant was supported by a grant which coveredtuitions, lodging, and meals.

The lectures and their subjects were as follows.Most of the lectures were ended with a tooldemonstration session.

• David Basin (Max-Planck Institut fur In-formatik, Saarbrucken, Germany): Verifi-cation Based on Monadic Logic, (4 hours).The lecture was centred on a new approachto hardware verification based on describ-ing circuits in monadic second-order logic(M2L). David Basin described the theoryand practice of how M2L, as embodiedin the MONA tool, can be used to auto-matically verify parameterised circuit de-signs. The representation of generic de-signs in this logic and the decision proce-dure, which reduces formulas to canonicalautomata, was demonstrated.

• Edmund M. Clarke (Carnegie-Mellon Uni-versity, Pittsburgh, USA): Symbolic ModelChecking, (4 hours). Ed Clarke startedwith an introduction to CTL, model check-ing, and binary decision diagrams. Thesecond part of the lecture then introducedus to the specification language SMV (Sym-bolic Model Checking). Specifications inSMV of a synchronous arbiter, an arbitercell, and a pipelined ALU served as exam-ples, which were verified in the SMV tooldemonstration.

• Thomas A. Henzinger (University of Cali-fornia at Berkeley, USA): Automatic Verifi-cation of Real-Time and Hybrid Systems (4hours). Thomas Henzinger introduced usto the theory of hybrid automaton, a for-mal model for dynamical systems with dis-crete and continuous components. He pre-sented several recent results and demon-strated that methods for the verification offinite-state systems can be used to anal-yse certain systems with uncountable statespace.

• Gerard J. Holzmann (Bell Laboratories,Murray Hill, USA): On-the-Fly ModelChecking Tutorial, (4 hours). This lecturegave an overview of the design and struc-ture of the SPIN verification tool. Ger-ard Holzmann reviewed the automata-theoretical foundations, and gave exam-ples of some typical applications of themodel checker in practise.

• Kim G. Larsen (BRICS, Aalborg, Den-mark): UPPAAL tool demonstration, (1hour). UPPAAL is a tool for symbolicsimulation and automatic verification ofreal-timed systems modelled as networksof timed automaton. The demonstrationshowed us how to simulate and verify asmall production line.

• Tom F. Melham (University of Glasgow,UK): Some Research Issues in Higher Or-der Logic Theorem Proving, (4 hours).

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Figure 1: The signing of the European Educational Forum contract. The three signatories from left toright: Ralph-Johan Back (TUCS), Mogens Nielsen (BRICS) and Jos Baeten (IPA) supervised by GrzegorzRozenberg (IPA), the chairman of the EEF Steering Committee.

Based on the experience of the HOL re-search community, Tom Melham talkedabout requirements of the design of inter-faces of verification tools, the embeddingof specialised languages into higher orderlogic supported by a theorem prover, andthe integration and implementation of au-tomated proof methods.

• Robert Pollack (University of Edinburgh,UK): What we Learn from Formal Check-ing, (4 hours). At first Robert Pollack dis-cussed the value of large machine-checkedproofs, proposing a view in which belief inmachine verifications is based on evidenceand asking whether a claimed proof is ac-tually a derivation in the claimed formalsystem, and whether what it proves is the

claimed theorem. He introduced us to typetheory, namely the use of inductive defini-tions to represent data types and relationsand the tool LEGO for checking proofs inthe Extended Calculus of Constructions.

• Mandayam K. Srivas (Computer ScienceLaboratory, SRI International, Menlo Park,USA): A Combined Approach to Hard-ware Verification: Proof-checking, Rewrit-ing with decision procedures and Model-checking, (4 hours). With the goal to il-lustrate how an integrated verification sys-tem that combines proof checking, rewrit-ing, decision procedures, and model check-ing can be used for effective hardware veri-fication, Mandayam Srivas started with thedesign philosophy of the Prototype Verifi-

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cation System (PVS). The second part of hislecture was concerned with the combina-tion of rewriting with decision proceduresand model checking with proof checking,and the problem of scaling up verificationto industrial design.

The series of lectures gave a wide overview ofthe area of verification based on model checkingand theorem proving, for ’newcomers’ as wellas for participants already familiar with the re-search area.

The lecture material was published in the BRICSNote Series ([NS-96-2] to [NS-96-12]).

On Wednesday afternoon we were taken to visitthe Aarhus museum of science. The schoolended with an excellent farewell dinner on Fri-day evening, held in the university restaurant.According to the tradition at Aarhus University,all participants performed together from time totime during the dinner several songs. The tra-dition of the last song required us to climb upthe dinner tables from verse to verse and so theschool was ended with all participants standingon the tables.

The organisation of the school was excellent. Inthe name of all participants let me thank the or-ganisers: Allan Cheng, Mogens Nielsen, and thesecretary: Karen.

European Educational Forum

The European Educational Forum (EEF) is a jointactivity of three research schools: BRICS, IPA (In-stitute for Programming Research and Algorith-mics) from the Netherlands, and TUCS (TurkuCentre for Computer Science) from Finland.

The goal of EEF is to organise various forms ofactivities covering a broad spectrum of Basic Re-search and Applications and aimed at the educa-tion of PhD’s and young researchers. The formof the activities may vary: it may take form of aworkshop, a school, a topic-focused conferenceor a conference presenting a number of topics

that are relevant in Basic Research and Applica-tions at the given moment.

The EEF was entered into contract (figure 1) dur-ing the first EEF-event, a School on EmbeddedSystems held in Veldhoven, The Netherlands,November 25–29, 1996.

For further information please see the EEF homepage: www.tucs.abo.fi/EEF.

Kiel Meeting

by Thomas T. Hildebrandt

A cold and wet morning, Tuesday December 3, anumber of BRICS people boarded a mini-bus atthe parking ground in front of the department,heading towards Kiel. The crowd, a rare mixtureof professors, post docs, PhD and grad. students(see picture) had signed up for a one-and-a-halfday visit to Kiel.

The scientific content of the trip was “some in-formal BRICS/Kiel talks” exposing the work ofeach group for the other. Five of us had volun-teered to give a talk on our current line of work,latest results or a theorem one hoped to provenext week.

The drive went as planned (and clearly, the con-versation in the bus was a lot more interestingthan the landscape). After a short stop at thecomputer science department in Kiel picking upthe Kiel group (see figure 2), we went to a pleas-ant conference building by the harbour.

Here a good solid lunch awaited us, openingup for an informal chat. Thereafter we delvedinto the first row of talks, continuing till late inthe afternoon, interrupted by coffee breaks and ariver-side walk. Later we went to a nice restau-rant (after a short walk in the city) and even laterto our comfortable hotel where we could rest af-ter a long, but elucidating day.

Wednesday morning we finished the series oftalks (10 in all) and headed home in high spirit,only with a short stop by the border buying var-ious kinds of liquid and non-liquid goods.

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Figure 2: Participants in the Kiel Meeting. From the left: Anders Sandholm, P. S. Thiagarajan, Thomas S.Hune, Marcin Jurdzinski, Jesper G. Henriksen, Nils Buhrke (Kiel), Wolfgang Thomas (Kiel), Jens Voge (Kiel),Thomas T. Hildebrandt, Margrit Krause (Kiel), Ina Schiering (Kiel), Erich Valkema (Kiel), Thomas Wilke(Kiel), Sebastian Seibert (Kiel), Glynn Winskel, Oliver Matz (Kiel), Prakash Panangaden, Uffe H. Engberg,Kousha Etessami, Helmut Lescow (Kiel).

The informal programme for the visit had madeit pleasant to listen to the many talks, whichwere an interesting mixture (some even on workthat grew into accepted papers for LICS ’97). Itgave us a good peep at the field of work doneby the group in Kiel, showing where it had anoverlap with research at BRICS—and hopefullyit worked equally well in the other direction.

Introduction to Linear Logic

Torben Brauner, BRICS, gave December 18, 1996,

an introduction to Linear Logic. The course alsocovered Classical and Intuitionistic Logic. Thecourse material appears as Lecture Series report[LS-96-6] below.

Distributed Logics

January 20–21, 1997, P. S. Thiagarajan, SPICMathematical Institute, Madras, India, gave acourse of two double lectures on DistributedLogics. Course description is on the web.

Newly Appointed Researchers and Guests

Carsten ButzCarsten Butz joined BRICS in January and is cur-rently giving a course on categorical logic. Heobtained his PhD degree from the Mathemat-ical Department of the University of Utrecht,The Netherlands, in 1996. In his thesis he used

topological models of infinitary first order the-ories to construct spaces that compute variouswell known cohomology theories (which are al-gebraic invariants). His recent research focuseson logic and category theory.

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Arne AnderssonArne Andersson received his PhD from LundUniversity in 1990 and he became a reader (“do-cent”) in computer science in 1994. His main re-search area is fundamental data structures. Inparticular, his research has been focused on fastalgorithms for sorting and searching. He alsostrives to combine simplicity with efficiency assimple methods are more likely to find their wayinto teaching and practice. Apart from his re-search interests, he is a committed teacher; in1991 he was awarded “best teacher” by the stu-dents at Lund University. Life is more thanwork, among other things he enjoys playing thetrumpet, as well as arranging and conductingmusic. Arne Andersson will spend every fourthweek at the BRICS PhD School and the remain-ing time at the Department of Computer Science,LTH (Lund Institute of Technology), Sweden.

Ulrich KohlenbachUlrich Kohlenbach got his PhD in 1990 from theDept. of Mathematics of the University Frank-furt where he became Privatdozent in 1995. Dur-ing the academic year 1996/97 he has been vis-iting assistant professor at the Department ofMathematics, University of Michigan, Ann Ar-bor. His main research interests so far havebeen in the area of proof theory with applica-tions to concrete proofs: extraction of effectivedata from ineffective proofs, transformations ofproofs and their complexity, proofs and func-tionals of finite type, intuitionistic reasoning,computational mathematics, (weak) fragmentsof arithmetic and analysis.Ulrich Kohlenbach will join BRICS in July 1997.

Alessandro PanconesiAlessandro Panconesi received his PhD in Com-puter Science from Cornell University in 1993.His thesis entitled “Locality in Distributed Com-puting” included work from a paper that wonthe Best Student Paper Award at the 1992 STOC.After returning to Europe, Alessandro held anERCIM Fellowship, spending 6 months each atAmsterdam, Trondheim and Stockholm. Hehad a von Humboldt Fellowship at Freie Uni-versitat, Berlin and is currently at Nada (Nu-

merical Analysis and Computing Science), KTH(Royal Institute of Technology), Stockholm, Swe-den. Alessandro Panconesi will join the BRICSPhD School in September 1997.

David TomanDavid Toman will be visiting BRICS in thefall ’97 semester. He will join the research atBRICS as well as give introductory lectures onDatabases. He received his M.S. (Mgr.) de-gree in computer science from Masaryk Uni-versity, Brno, Czech Republic, in 1992 and hisPhD from Kansas State University in 1996. Cur-rently he is a NATO/NSERC Postdoctoral Fel-low at the University of Toronto, Canada. Hisresearch interests include temporal, deductive,and constraint databases, logic-based languagesfor database and information systems, formalmethods, logic programming (and other non-imperative paradigms), and programming lan-guages. In his spare time he also likes to hackFreeBSD on his tiny Toshiba Libretto laptop.

Uwe NestmannUwe Nestmann’s main interests are the seman-tics of concurrent and distributed computationand, in particular, calculi for mobile processes.He has received his PhD degree in 1996 fromthe University of Erlangen-Nurnberg, Germany,for a dissertation on “determinacy and nonde-terminacy” in the context of Pict, the concurrentimplementation of the asynchronous π-calculus,where he focused on the investigation of choiceencodings and type systems for detecting con-fluent behaviours. The PhD was carried outin tight collaboration with Benjamin Pierce dur-ing numerous visits at the Universities of Ed-inburgh and Cambridge, and finalised duringa 6 month stay at INRIA Sophia-Antipolis. Heis currently an ERCIM post-doc at INRIA Roc-quencourt, where the distributed implementa-tion of the π-calculus is developed, known as thejoin-calculus, so his current interests include dis-tributed computing.Uwe Nestmann will join BRICS in Aalborg in Oc-tober 1997.

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Augusto Burgueno ArjonaAugusto Burgueno Arjona is a PhD studentat CERT (Centre d’Etudes et de Recherches deToulouse), France. His research interests in-clude real-time process algebras and verificationof real-time systems and recently he is workingon an extension of hybrid automata called Slope-Parametric Hybrid Automata (SPHA). He willbe visiting BRICS in Aalborg from June to Au-gust as a BRICS summer student and work onintegrating ideas of SPHA in the UPPAAL toolsuit.

Vincent BalatVincent Balat is a PhD student of Chris-tine Paulin-Mohring from the Ecole NormaleSuperieure at Lyon, France. He will visit BRICS

in July and August as a BRICS summer student.He will work on the lambda-calculus as a meta-language. Aside from his interest in theoreticalcomputer science, Vincent also has a degree inoboe and cor anglais.

Zhe YangZhe Yang is a PhD student of Robert Paige atCourant Institute of Mathematical Science, NewYork University, USA. His research focuses onareas such as programmming languages andprogram transformation techniques. His currentinterest is in applying various qualitative meth-ods in programming languages to get quantita-tive improvements in algorithms. Zhe Yang willvisit BRICS from mid August to the end of De-cember 1997.

Dissertation AbstractsWorst Case Efficient Data Structures

by Gerth Stølting Brodal

We study the design of efficient data structures.In particular we focus on the design of datastructures where each operation has a worst caseefficient implementations. The concrete prob-lems we consider are partial persistence, imple-mentation of priority queues, and implementationof dictionaries.

The first problem we consider is how to makebounded in-degree and out-degree data struc-tures partially persistent, i.e., how to rememberold versions of a data structure for later access. Anode copying technique of Driscoll et al. supportsupdate steps in amortized constant time and ac-cess steps in worst case constant time. The worstcase time for an update step can be linear in thesize of the structure. We show how to extend thetechnique of Driscoll et al. such that update stepscan be performed in worst case constant time onthe pointer machine model.

We present two new comparison based prior-ity queue implementations, with the followingproperties. The first implementation supports

the operations FINDMIN, INSERT and MELDin worst case constant time and DELETE andDELETEMIN in worst case timeO(logn). The pri-ority queues can be implemented on the pointermachine and require linear space. The sec-ond implementation achieves the same worstcase performance, but furthermore supportsDECREASEKEY in worst case constant time. Thespace requirement is again linear, but the im-plementation requires auxiliary arrays of sizeO(logn). Our bounds match the best knownamortized bounds (achieved by respectively bi-nomial queues and Fibonacci heaps). The datastructures presented are the first achieving theseworst case bounds, in particular supportingMELD in worst case constant time. We showthat these time bounds are optimal for all im-plementations supporting MELD in worst casetime o(n). We also present a tradeoff between theupdate time and the query time of comparisonbased priority queue implementations. Finallywe show that any randomized implementationwith expected amortized cost t comparisons perINSERT and DELETE operation has expected costat least n/2O(t) comparisons for FINDMIN.

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Next we consider how to implement priorityqueues on parallel (comparison based) mod-els. We present time and work optimal priorityqueues for the CREW PRAM, supporting FIND-MIN, INSERT, MELD, DELETEMIN, DELETE andDECREASEKEY in constant time with O(logn)processors. Our implementation is the first sup-porting all of the listed operations in constanttime. To be able to speed up Dijkstra’s algo-rithm for the single-source shortest path prob-lem we present a different parallel priority datastructure. With this specialized data structurewe give a parallel implementation of Dijkstra’salgorithm which runs in O(n) time and per-forms O(m logn) work on a CREW PRAM. Thisrepresents a logarithmic factor improvement forthe running time compared with previous ap-proaches.

We also consider priority queues on a RAMmodel which is stronger than the comparisonmodel. The specific problem is the maintenanceof a set of n integers in the range 0..2w − 1 un-der the operations INSERT, DELETE, FINDMIN,FINDMAX and PRED (predecessor query) on aunit cost RAM with word size w bits. TheRAM operations used are addition, left and rightbit shifts, and bit-wise boolean operations. Forany function f(n) satisfying log log n ≤ f(n) ≤√

log n, we present a data structure supportingFINDMIN and FINDMAX in worst case constanttime, INSERT and DELETE in worst case O(f(n))time, and PRED in worst case O((logn)/f(n))time. This represents the first priority queueimplementation for a RAM which supports IN-SERT, DELETE and FINDMIN in worst case timeO(log logn) — previous bounds were only amor-tized. The data structure is also the first dic-tionary implementation for a RAM which sup-ports PRED in worst case O(logn/ log log n) timewhile having worst case O(log log n) updatetime. Previous sublogarithmic dictionary imple-mentations do not provide for updates that aresignificantly faster than queries. The best solu-tions known support both updates and queriesin worst case time O(

√logn).

The last problem consider is the following dictio-nary problem over binary strings. Given a set ofn binary strings of length m each, we want to an-swer d–queries, i.e., given a binary query stringof length m to report if there exists a string inthe set within Hamming distance d of the querystring. We present a data structure of sizeO(nm)supporting 1–queries in time O(m) and the re-porting of all strings within Hamming distance1 of the query string in time O(m). The datastructure can be constructed in time O(nm). Theimplementation presented is the first achievingthese optimal time bounds for the preprocess-ing of the dictionary and for 1–queries. The datastructure can be extended to support the inser-tion of new strings in amortized time O(m).

Trust and Dependence Analysis

by Peter Ørbæk

The two pillars of trust analysis and dependencealgebra form the foundation of this thesis. Trustanalysis is a static analysis of the run-time trust-worthiness of data. Dependence algebra is a richabstract model of data dependences in program-ming languages, applicable to several kinds ofanalyses.

Trust analysis tracks the data flow in a programwith the aim of ensuring that appropriate vali-dation checks are made on all data paths leadingto “dangerous” operations, such as entering datainto a private database, deleting files, etc.

Computers are increasingly being used to handleimportant transactions across the Internet. Le-gal documents and money orders are sent acrossthe same network as is used to transfer e-mailand non-business related information. Thus sep-arating these two kinds of information is becom-ing more and more of an issue. This problemis usually attacked using encryption and digitalsignatures for the important information flowsbetween computers. But what if there, some-where inside a program, is a data path betweenthe reading of a message from the network and

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a dangerous operation depending on that mes-sage, such that the signature of the message isnot checked on that path?

An example of an application where itis important to perform validity checks isin an HTTP (Hypertext Transfer Protocol[RFC1945,RFC2068]) server. Most such serversallow separate programs (so-called CGI scripts,for Common Gateway Interface) to be started onthe server machine in response to requests fromclients. The usual convention is that the webbrowser requests an URL of the form “http:-//www.company.com/cgi-bin/ program” tostart program. A CGI script can in principle beany program, so it is important that the serverprocess checks that the requested program is oneof the few programs allowed to be executed inthis manner. In a complicated server programthere are many data paths from the receptionof an URL to the command to be executed. Itis important that the checks for allowed pro-grams are done on all these data paths. Trustanalysis has been developed with the goal thata compiler will be able to provide the program-mer with a guarantee that checks are presenton all data paths between the reception of un-trusted input and the execution of commandswhere only trustworthy (checked, validated) in-formation should be present.

Since we want our analysis to be generally appli-cable, we do not consider the very specific teststhat have to be done on input data in varioussituations, such as checking digital signaturesor verifying pathnames against a known pat-tern. Devising these tests is still up to the care-ful program designer. Instead our analysis offersa “trust ” construct that is meant to be appliedto data after they have passed the specific valid-ity checks, the analysis will then propagate thisknowledge around the program. At points of theprogram where something dangerous is aboutto happen, such as starting another program orstarting a transaction against a database, the pro-grammer can write a “check ” construct to en-sure that the arguments can indeed be trusted,which means that they only depend on data that

have actually passed the validity checks.

Dependence analysis is a more general frame-work that can be applied to different concreteanalysis tasks. The data flow in a programis modeled as channels with certain proper-ties determining which kinds of data can passthrough the channels. Mathematically, a de-pendence algebra is a semi-lattice ordered semi-ring with certain additional axioms. Vectorspaces over such algebras are studied, and a non-trivial construction of a dependence algebra fora may/must analysis is given.

One of the virtues of dependence algebra-basedanalysis is that, by emphasising the connectionsbetween slots manifest in the program, the anal-ysis can be program-point sensitive. In type sys-tems the underlying idea is to associate a type toeach slot, such that a given slot is associated witha fixed (possibly polymorphic) type throughoutthe program. In contrast to this, a dependence-based analysis may allow a slot to hold differ-ent types of values at different points in the pro-gram without sacrificing detailed knowledge ofthe type of value in the slot at those points.

Contributions

The thesis introduces the notion of trust analy-sis, and studies its application to different kindsof languages. First a trust analysis for a simpleWHILE language is given, both in the form of anabstract interpretation, and as a constraint gen-eration problem. Then a trust analysis for an ex-tended λ-calculus is given in the form of a typesystem, together with a type inference algorithmbased on constraints (this part of the thesis isjoint work with Jens Palsberg). Finally, an imple-mentation of a trust analysis for the C program-ming language is described. The implementa-tion is based on the dependence algebra technol-ogy.

The second contribution of the thesis is the de-velopment of the dependence algebra frame-work for program analyses. The algebraic frame-work is applied in the trust analyser for C, as

12

well as for a soft type inference algorithm for ac-tion semantic equations.

An Axiomatic Approach to Adequacy

by Torben Brauner

This thesis studies adequacy for PCF-like lan-guages in a general categorical framework.PCF (Programming language for ComputableFunctions) is a programming language basedon a Curry-Howard interpretation of Intuition-istic Logic, namely the well-known typed λ-calculus, augmented with numerals and fixpointconstants. An adequacy result relates the de-notational semantics of a program to its oper-ational semantics; it typically states that a pro-gram terminates whenever the interpretation isnon-bottom. The main concern of the thesis is togeneralise to a linear version of PCF, called Lin-ear PCF, the adequacy results known for stan-dard PCF, keeping in mind that there exists aGirard translation from PCF to Linear PCF withrespect to which the new constructs should besound. Linear PCF is obtained by augmentinga Curry-Howard interpretation of IntuitionisticLinear Logic with numerals and fixpoint con-stants, appropriate for the linear context.

General adequacy results have usually been ob-tained in order-enriched categories, that is, cat-egories where all hom-sets are typically cpos,maps are assumed to be continuous and fix-point constants are interpreted using least up-per bounds. One of the main contributions ofthe thesis is to propose a completely different ap-proach to the problem of axiomatising those cat-egories which yield adequate semantics for PCFand Linear PCF. Historically, the axioms of ourcategorical model were discovered essentially byextracting the properties of the order-structureof an order-enriched categorical model whichare actually used to obtain an adequacy result.The order-structure is used to define fixpointssuch that for any endomap f the chain of finiteapproximants ⊥; fnn∈ω actually approximates

the fixpoint f] in an appropriate sense. So ratherthan assume the presence of an order-structure,we axiomatise what is actually needed; namelyfixpoints which are approximated by their (for-mal) finite approximants in an appropriate sensestated in non-order-theoretic terms.

The starting point of our axiomatisation is acartesian closed category where for each objectBwe assume the presence of an “undefined” map⊥B: 1 → B together with a fixpoint operator, thatis, an operation which to a map f : B → B as-signs a map f ] : 1 → B such that f] = f ]; f . Wealso assume the presence of an object N togetherwith appropriate maps for dealing with numer-als. The categorical axioms consist of a coupleof equational (that is, first order) ones togetherwith one non-equational, namely the axiom ofrational openness on each fixpoint operator. Afixpoint operator is rationally open with respectto an object P iff for all maps f : B → B andg : B → P it is the case that

f ]; g 6=⊥ ⇒ ∃n ∈ ω. ⊥; fn; g 6=⊥ .

It is shown that this axiom is sufficient, and in aprecise sense necessary, for adequacy. Thus, thehidden essential property of an order-theoreticmodel has been revealed: Definedness of anexpression is determined by the (formal) finiteapproximants to the involved fixpoints. It isfurthermore shown that our axioms induce anorder-theoretic categorical model in a canonicalway.

These ideas are developed in the intuitionisticcase (standard PCF) as well as in the linear case(Linear PCF). Two concrete categories satisfyingthe axioms of the categorical model are given,namely the category of cpos and (strict) contin-uous functions, and the category of dI-domainsand (linear) stable functions. Using instantia-tions to concrete models of the general adequacyresults, various purely syntactic properties ofLinear PCF are proved to hold.

Published as BRICS dissertation DS-96-4.

13

New in the BRICS Report Series, 1997 and 1996 ISSN 0909-0878

9 Jesper G. Henriksen and P. S. Thiagarajan. AProduct Version of Dynamic Linear Time Tempo-ral Logic. April 1997. 18 pp. To appear in Con-currency Theory: 7th International Conference,CONCUR ’97 Proceedings, LNCS, 1997.

8 Jesper G. Henriksen and P. S. Thiagarajan.Dynamic Linear Time Temporal Logic. April1997. 33 pp.

7 John Hatcliff and Olivier Danvy. Thunks andthe λ-Calculus (Extended Version). March 1997.55 pp. Extended version of article to appearin the Journal of Functional Programming.

6 Olivier Danvy and Ulrik P. Schultz. Lambda-Dropping: Transforming Recursive Equationsinto Programs with Block Structure. March1997. 53 pp. Extended version of an articleto appear in the 1997 ACM SIGPLAN Sym-posium on Partial Evaluation and Semantics-Based Program Manipulation (PEPM ’97),Amsterdam, The Netherlands, June 1997.

5 Kousha Etessami, Moshe Y. Vardi, andThomas Wilke. First-Order Logic with TwoVariables and Unary Temporal. March 1997. Toappear in Twelfth Annual IEEE Symposium onLogic in Computer Science, LICS ’97 Proceed-ings.

4 Richard Blute, Josee Desharnais, AbbasEdalat, and Prakash Panangaden. Bisimula-tion for Labelled Markov Processes. March 1997.48 pp. To appear in Twelfth Annual IEEE Sym-posium on Logic in Computer Science, LICS ’97Proceedings.

3 A Definability Theorem for First Order Logic.Butz, Carsten and Moerdijk, Ieke. March 1997.10 pp.

2 David A. Schmidt. Abstract Interpretation inthe Operational Semantics Hierarchy. March1997. 33 pp.

1 Olivier Danvy and Mayer Goldberg. PartialEvaluation of the Euclidian Algorithm (ExtendedVersion). January 1997. 16 pp.

62 P. S. Thiagarajan and Igor Walukiewicz. AnExpressively Complete Linear Time TemporalLogic for Mazurkiewicz Traces. December1996. i+13 pp. To appear in Twelfth AnnualIEEE Symposium on Logic in Computer Science,LICS ’97 Proceedings.

61 Sergei Soloviev. Proof of a Conjecture of S. MacLane. December 1996. 53 pp. Extended ab-stract appears in Pitt, Rydeheard and John-stone, editors, Category Theory and ComputerScience: 6th International Conference, CTCS ’95Proceedings, LNCS 953, 1995, pages 59–80.

60 Johan Bengtsson, Kim G. Larsen, FredrikLarsson, Paul Pettersson, and Wang Yi. UP-PAAL in 1995. December 1996. 5 pp. Ap-pears in Margaria and Steffen, editors, Toolsand Algorithms for The Construction and Anal-ysis of Systems: 2nd International Workshop,TACAS ’96 Proceedings, LNCS 1055, 1996,pages 431–434.

59 Kim G. Larsen, Paul Pettersson, and Wang Yi.Compositional and Symbolic Model-Checking ofReal-Time Systems. December 1996. 12 pp.Appears in 16th IEEE Real-Time Systems Sym-posium, RTSS ’95 Proceedings, 1995.

58 Johan Bengtsson, Kim G. Larsen, FredrikLarsson, Paul Pettersson, and Wang Yi. UP-PAAL — a Tool Suite for Automatic Verificationof Real–Time Systems. December 1996. 12 pp.Appears in Alur, Henzinger and Sontag, ed-itors, DIMACS Workshop on Verification and

14

Control of Hybrid Systems, HYBRID ’96 Pro-ceedings, LNCS 1066, 1996, pages 232–243.

57 Kim G. Larsen, Paul Pettersson, and WangYi. Diagnostic Model-Checking for Real-TimeSystems. December 1996. 12 pp. Appearsin Alur, Henzinger and Sontag, editors, DI-MACS Workshop on Verification and Controlof Hybrid Systems, HYBRID ’96 Proceedings,LNCS 1066, 1996, pages 575–586.

56 Zine-El-Abidine Benaissa, Pierre Lescanne,and Kristoffer H. Rose. Modeling Sharing andRecursion for Weak Reduction Strategies usingExplicit Substitution. December 1996. 35 pp.Appears in Kuchen and Swierstra, editors,8th International Symposium on ProgrammingLanguages, Implementations, Logics, and Pro-grams, PLILP ’96 Proceedings, LNCS 1140,1996, pages 393–407.

55 Kare J. Kristoffersen, Francois Laroussinie,Kim G. Larsen, Paul Pettersson, and WangYi. A Compositional Proof of a Real-Time Mu-tual Exclusion Protocol. December 1996. 14 pp.To appear in Dauchet and Bidoit, editors, The-ory and Practice of Software Development. 7th In-ternational Joint Conference CAAP/FASE, TAP-SOFT ’97 Proceedings, LNCS, 1997.

54 Igor Walukiewicz. Pushdown Processes: Gamesand Model Checking. December 1996. 31 pp.Appears in Alur and Henzinger, editors,8th International Conference on Computer-AidedVerification, CAV ’96 Proceedings, LNCS 1102,1996, pages 62–74.

53 Peter D. Mosses. Theory and Practice of Ac-tion Semantics. December 1996. 26 pp. Ap-pears in Penczek and Szalas, editors, Mathe-matical Foundations of Computer Science: 21stInternational Symposium, MFCS ’96 Proceed-ings, LNCS 1113, 1996, pages 37–61.

52 Claus Hintermeier, Helene Kirchner, and Pe-ter D. Mosses. Combining Algebraic and Set-Theoretic Specifications (Extended Version). De-cember 1996. 26 pp. Appears in Haveraaen,Owe and Dahl, editors, Recent Trends in Data

Type Specification: 11th Workshop on Specifica-tion of Abstract Data Types, joint with 8th COM-PASS Workshop, Selected Papers, LNCS 1130,1996, pages 255–274.

51 Claus Hintermeier, Helene Kirchner, and Pe-ter D. Mosses. Rn- and Gn-Logics. Decem-ber 1996. 19 pp. Appears in Gilles, Heer-ing, Meinke and Moller, editors, Higher-OrderAlgebra, Logic, and Term-Rewriting: 2nd In-ternational Workshop, HOA ’95 Proceedings,LNCS 1074, 1996, pages 90–108.

50 Aleksandar Pekec. Hypergraph OptimizationProblems: Why is the Objective Function Linear?December 1996. 10 pp.

49 Dan S. Andersen, Lars H. Pedersen, HansHuttel, and Josva Kleist. Objects, Types andModal Logics. December 1996. 20 pp. Tobe presented at the 4th International Workshopon the Foundations of Object-Oriented, FOOL4,1997.

48 Aleksandar Pekec. Scalings in Linear Program-ming: Necessary and Sufficient Conditions for In-variance. December 1996. 28 pp.

47 Aleksandar Pekec. Meaningful and Meaning-less Solutions for Cooperative N-person Games.December 1996. 28 pp.

46 Alexander E. Andreev and Sergei Soloviev.A Decision Algorithm for Linear Isomorphism ofTypes with ComplexityCn(log2(n)). November1996. 16 pp.

45 Ivan B. Damgard, Torben P. Pedersen, andBirgit Pfitzmann. Statistical Secrecy and Multi-Bit Commitments. November 1996. 30 pp.To appear in IEEE Transactions on InformationTheory.

44 Glynn Winskel. A Presheaf Semantics of Value-Passing Processes. November 1996. 23 pp. Ex-tended and revised version of paper appear-ing in Montanari and Sassone, editors, Con-currency Theory: 7th International Conference,CONCUR ’96 Proceedings, LNCS 1119, 1996,pages 98–114.

15

43 Anna Ingolfsdottir. Weak Semantics Based onLighted Button Pressing Experiments: An Alter-native Characterization of the Readiness Seman-tics. November 1996. 36 pp. Extended ab-stract presented at the 10th Annual Interna-tional Conference of the European Association forComputer Science Logic, CSL ’96.

42 Gerth Stølting Brodal and Sven Skyum. TheComplexity of Computing the k-ary Compositionof a Binary Associative Operator. November1996. 15 pp.

41 Stefan Dziembowski. The Fixpoint Bounded-Variable Queries are PSPACE-Complete.November 1996. 16 pp. Presented at the 10thAnnual International Conference of the EuropeanAssociation for Computer Science Logic, CSL ’96.

40 Gerth Stølting Brodal, Shiva Chaudhuri,and Jaikumar Radhakrishnan. The Random-ized Complexity of Maintaining the Minimum.November 1996. 20 pp. To appear in a specialissue of Nordic Journal of Computing devotedto the proceedings of SWAT ’96. Appears inKarlson and Lingas, editors, Algorithm The-ory: 5th Scandinavian Workshop, SWAT ’96 Pro-ceedings, LNCS 1097, 1996, pages 4–15.

39 Hans Huttel and Sandeep Shukla. On theComplexity of Deciding Behavioural Equiva-lences and Preorders – A Survey. October 1996.36 pp.

38 Hans Huttel and Josva Kleist. Objects as Mo-bile Processes. October 1996. 23 pp. Pre-sented at the 12th Annual Workshop on Mathe-matical Foundations of Programming Languages,MFPS ’96, (Boulder, Colorado, USA, June 3–5, 1996).

37 Gerth Stølting Brodal and Chris Okasaki. Op-timal Purely Functional Priority Queues. Octo-ber 1996. 27 pp. To appear in Journal of Func-tional Programming, 6(6), December 1996.

36 Luca Aceto, Willem Jan Fokkink, and AnnaIngolfsdottir. On a Question of A. Salomaa: TheEquational Theory of Regular Expressions over a

Singleton Alphabet is not Finitely Based. Octo-ber 1996. 16 pp.

35 Gian Luca Cattani and Glynn Winskel.Presheaf Models for Concurrency. October 1996.16 pp. Presented at the 10th Annual Interna-tional Conference of the European Association forComputer Science Logic, CSL ’96.

34 John Hatcliff and Olivier Danvy. A Computa-tional Formalization for Partial Evaluation (Ex-tended Version). October 1996. 67 pp. To ap-pear in Mathematical Structures in ComputerScience.

33 Jonathan F. Buss, Gudmund SkovbjergFrandsen, and Jeffrey Outlaw Shallit. TheComputational Complexity of Some Problems ofLinear Algebra. September 1996. 39 pp. Re-vised version to appear in STACS ’97: 14thAnnual Symposium on Theoretical Aspects ofComputer Science Proceedings, LNCS, 1997.

32 P. S. Thiagarajan. Regular Trace Event Struc-tures. September 1996. 34 pp.

31 Ian Stark. Names, Equations, Relations: Prac-tical Ways to Reason about ‘new’. September1996. ii+22 pp. To appear in Typed Lambda Cal-culi and Applications: 3rd International Confer-ence, TLCA ’97 Proceedings, LNCS, 1997.

30 Arne Andersson, Peter Bro Miltersen, andMikkel Thorup. Fusion Trees can be Imple-mented with AC0 Instructions only. September1996. 8 pp.

29 Lars Arge. The I/O-Complexity of OrderedBinary-Decision Diagram Manipulation. Au-gust 1996. 35 pp. An extended abstract ver-sion appears in Staples, Eades, Kato, andMoffat, editors, Algorithms and Computation:6th International Symposium, ISAAC ’95 Pro-ceedings, LNCS 1004, 1995, pages 82–91.

28 Lars Arge. The Buffer Tree: A New Technique forOptimal I/O Algorithms. August 1996. 34 pp.This report is a revised and extended versionof the BRICS Report RS-94-16. An extended

16

abstract appears in Akl, Dehne, Sack, andSantoro, editors, Algorithms and Data Struc-tures: 4th Workshop, WADS ’95 Proceedings,LNCS 955, 1995, pages 334–345.

27 Devdatt P. Dubhashi, Volker Priebe, andDesh Ranjan. Negative Dependence Through theFKG Inequality. July 1996. 15 pp.

26 Nils Klarlund and Theis Rauhe. BDD Algo-rithms and Cache Misses. July 1996. 15 pp.

25 Devdatt P. Dubhashi and Desh Ranjan. Ballsand Bins: A Study in Negative Dependence. July1996. 27 pp.

New in the BRICS Notes Series, 1996 ISSN 0909-3206

15 CoFI. CASL – The CoFI Algebraic SpecificationLanguage; Tentative Design: Language Sum-mary. December 1996. viii+34 pp.

14 Peter D. Mosses. A Tutorial on Action Seman-tics. December 1996. 46 pp. Tutorial notes forFME ’94 (Formal Methods Europe, Barcelona,1994) and FME ’96 (Formal Methods Europe,Oxford, 1996).

13 Olivier Danvy, editor. Proceedings of the Sec-ond ACM SIGPLAN Workshop on Continua-tions, CW ’97 (ENS, Paris, France, 14 January,1997), December 1996. 166 pp.

12 Mandayam K. Srivas. A Combined Ap-proach to Hardware Verification: Proof-Checking,Rewriting with Decision Procedures and Model-Checking; Part II: Articles. BRICS AutumnSchool on Verification. October 1996. 56 pp.

11 Mandayam K. Srivas. A Combined Ap-proach to Hardware Verification: Proof-Checking,Rewriting with Decision Procedures and Model-Checking; Part I: Slides. BRICS Autumn Schoolon Verification. October 1996. 29 pp.

10 Robert Pollack. What we Learn from FormalChecking; Part III: Formalization is Not Just Fill-ing In Details. BRICS Autumn School on Verifi-cation. October 1996. iv+42 pp.

9 Robert Pollack. What we Learn from FormalChecking; Part II: Using Type Theory: An Intro-

duction. BRICS Autumn School on Verification.October 1996. iv+71 pp.

8 Robert Pollack. What we Learn from FormalChecking; Part I: How to Believe a Machine-Checked Proof. BRICS Autumn School on Veri-fication. October 1996. iv+19 pp.

7 Tom F. Melham. Some Research Issues in HigherOrder Logic Theorem Proving. BRICS AutumnSchool on Verification. October 1996. 15 pp.

6 Gerard J. Holzmann. On-the-Fly Model Check-ing Tutorial. BRICS Autumn School on Verifica-tion. October 1996. 31 pp.

5 Thomas A. Henzinger. Automatic Verifica-tion of Real-Time and Hybrid Systems. BRICSAutumn School on Verification. October 1996.28 pp.

4 Edmund M. Clarke, Jr. Symbolic Model Check-ing. BRICS Autumn School on Verification. Oc-tober 1996. 55 pp.

3 David A. Basin. Verification Based on MonadicLogic. BRICS Autumn School on Verification.October 1996. 43 pp.

2 Allan Cheng, Kim G. Larsen, and MogensNielsen, editors. Programme and Abstractsof the BRICS Autumn School on Verification(Aarhus, Denmark, October 28 – November1, 1996), August 1996. ii+18pp.

17

BRICS Lecture Series, 1996 ISSN 1395-2048

6 Torben Brauner. Introduction to Linear Logic.December 1996. iiiv+55 pp.

AbstractThe main concern of this report is to give anintroduction to Linear Logic. For pedagogicalpurposes we shall also have a look at Classi-cal Logic as well as Intuitionistic Logic. LinearLogic was introduced by J.-Y. Girard in 1987and it has attracted much attention from com-puter scientists, as it is a logical way of copingwith resources and resource control. The focusof this technical report will be on proof-theoryand computational interpretation of proofs,that is, we will focus on the question of howto interpret proofs as programs and reduction(cut-elimination) as evaluation. We first intro-duce Classical Logic. This is the fundamen-tal idea of the proofs-as-programs paradigm.Cut-elimination for Classical Logic is highlynon-deterministic; it is shown how this canbe remedied either by moving to Intuitionis-tic Logic or to Linear Logic. In the case onLinear Logic we consider Intuitionistic LinearLogic as well as Classical Linear Logic. Fur-thermore, we take a look at the Girard Trans-lation translating Intuitionistic Logic into In-tuitionistic Linear Logic. Also, we give a briefintroduction to some concrete models of In-tuitionistic Linear Logic. No proofs will begiven except that a proof of cut-elimination forthe multiplicative fragment of Classical LinearLogic is included in an appendix.

Contents

1 Classical and Intuitionistic Logic

1.1 Classical Logic1.2 Intuitionistic Logic1.3 The λ-Calculus1.4 The Curry-Howard Isomorphism

2 Linear Logic

2.1 Classical Linear Logic2.2 Intuitionistic Linear Logic

2.3 A Digression - Russell’s Paradox andLinear Logic

2.4 The Linear λ-Calculus2.5 The Curry-Howard Isomorphism2.6 The Girard Translation2.7 Concrete Models

A Logics

A.1 Classical LogicA.2 Intuitionistic LogicA.3 Classical Linear LogicA.4 Intuitionistic Linear Logic

B Cut-Elimination for Classical LinearLogic

B.1 Some Preliminary ResultsB.2 Putting the Proof Together.

5 Devdatt P. Dubhashi. What Can’t You Do WithLP? December 1996. viii+23 pp.

AbstractThese notes from the BRICS course “Pearlsof Theory” are an introduction to Linear Pro-gramming and its use in solving problems inCombinatorics and in the design and analysisof algorithms for combinatorial problems.

Contents

1 Dr. Cheng’s Diet and LP

2 LP versus NP: A Panacea?

3 Duality

4 Linear versus Integer

5 Luck: Unimodularity

6 Rounding

7 Randomised Rounding

8 Primal–Dual

9 If You Want to Prospect for more Pearls ...

10 Problems.

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4 Sven Skyum. A Non-Linear Lower Boundfor Monotone Circuit Size. December 1996.viii+14 pp.

Abstract

In complexity theory we are faced with thefrustrating situation that we are able to provevery few non trivial lower bounds. In the areaof combinatorial complexity theory which thisnote is about, the situation can be describedquite precisely in the sense that although al-most all functions are very complex (have ex-ponential circuit size), no one has been able toprove any non-linear lower bounds for explic-itly given functions.One alley which is often taken is to restrictthe models to make larger lower bounds morelikely. Until 1985 no non-linear lower boundswere known for monotone circuit size ei-ther (the best lower bound was 4n). In 1985,Razborov [1] proved a super polynomial lowerbound for a specific family of Boolean func-tions.Razborov proved the following:

Any family of monotone Booleancircuits accepting graphs containingcliques of size bn/2c has super poly-nomial size when the graphs are rep-resented by their incidence matrices.

The main purpose of this note is to give a “sim-ple” version of Razborov’s proof. This leads toa weaker result but the proof contains all theingredients of Razborov’s proof.We will prove:

Any family of monotone Booleancircuits accepting graphs containingcliques of size 3 (triangles) has sizeΩ(n3/ log4 n).

In Section 1 we introduce Boolean functionsand the complexity model we are going to use,namely Boolean circuits. In Section 2 the ap-propriate definitions of graphs are given andsome combinatorial properties about them are

proven. Section 3 contains the proof of themain result.

[1] A. A. Razborov: Lower bounds on themonotone complexity of some Booleanfunctions, Dokl. Akad. Nauk SSSR 281(4)(1985) 798 - 801 (In Russian); English trans-lation in: Soviet Math. Dokl. 31 (1985) 354–57.

Contents

1 Boolean functions and circuits

2 Graphs and Combinatorial lemmas

3 Putting things together

4 Problems.

3 Kristoffer H. Rose. Explicit Substitution – Tuto-rial & Survey. September 1996. v+150 pp.

AbstractThese lecture notes are from the BRICS mini-course “Explicit Substitution” taught at Uni-versity of Aarhus, October 27, 1996.We give a coherent overview of the area of ex-plicit substitution and some applications. Thefocus is on the operational or syntactic side ofthings, in particular we will not cover the areasof semantics and type systems for explicit sub-stitution calculi. Emphasis is put on providinga universal understanding of the very differ-ent techniques used by various authors in thearea.

Contents

1 Explicit Substitution Rules

1.1 Explicit Substitution1.2 Preservation of Strong Normalisation

(PSN)1.3 Discussion

2 Explicit Binding

2.1 Namefree λ-Calculus2.2 Explicit Binding Variations for Ex-

plicit Substitution2.3 Discussion

19

3 Explicit Addresses

3.1 λ-graphs and Explicit Sharing3.2 Explicit Substitution & Sharing3.3 Discussion

4 Higher-Order Rewriting and FunctionalPrograms

4.1 Combinatory Reduction Systems(CRS)

4.2 Explicit Substitutes4.3 Explicit Addresses4.4 CRS and Functional Programs4.5 Discussion

5 Strategies and Abstract Machines

5.1 Strategies for λ-Calculus5.2 Calculi for Weak Reduction with

Sharing5.3 Reduction Strategies5.4 Constructors and Recursion5.5 A Space Leak Free Calculus5.6 Discussion

A Appendices: Preliminaries

A.1 ReductionsA.2 Inductive NotationsA.3 λ-Calculus.

2 Susanne Albers. Competitive Online Algorithms.September 1996. iix+57 pp.

Abstract

These lecture notes are from the mini-course“Competitive Online Algorithms” taught atAarhus University, August 27–29, 1996.The mini-course consisted of three lectures. Inthe first lecture we gave basic definitions andpresented important techniques that are usedin the study on online algorithms. The pag-ing problem was always the running exam-ple to explain and illustrate the material. Wealso discussed the k-server problem, which isa very well-studied generalisation of the pag-ing problem.

The second lecture was concerned with self-organising data structures, in particular self-organising linear lists. We presented resultson deterministic and randomised online algo-rithms. Furthermore, we showed that linearlists can be used to build very effective datacompression schemes and reported on theoret-ical as well as experimental results.In the third lecture we discussed three appli-cation areas in which interesting online prob-lems arise. The areas were (1) distributed datamanagement, (2) scheduling and load balanc-ing, and (3) robot navigation and exploration.In each of these fields we gave some importantresults.

Contents

1 Online algorithms and competitive anal-ysis1.1 Basic definitions1.2 Results on deterministic paging algo-

rithms2 Randomisation in online algorithms

2.1 General concepts2.2 Randomised paging algorithms

against oblivious adversaries3 Proof techniques

3.1 Potential functions3.2 Yao’s minimax principle

4 The k-server problem5 The list update problem

5.1 Deterministic online algorithms5.2 Randomised online algorithms5.3 Average case analyses of list update

algorithms6 Data compression based on linear lists

6.1 Theoretical results6.2 Experimental results6.3 The compression algorithm by Bur-

rows and Wheeler7 Distributed data management

7.1 Formal definition of migration andreplication problems

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7.2 Page migration7.3 Page replication7.4 Page allocation

8 Scheduling and load balancing

8.1 Scheduling8.2 Load balancing

9 Robot navigation and exploration.

1 Lars Arge. External-Memory Algorithms withApplications in Geographic Information Systems.September 1996. iix+53 pp.

AbstractIn the design of algorithms for large-scale ap-plications it is essential to consider the prob-lem of minimising Input/Output (I/O) com-munication. Geographical information sys-tems (GIS) are good examples of such large-scale applications as they frequently handlehuge amounts of spatial data. In this note wesurvey the recent developments in external-memory algorithms with applications in GIS.First we discuss the Aggarwal-Vitter I/O-model and illustrate why normal internal-memory algorithms for even very simpleproblems can perform terribly in an I/O-environment. Then we describe the funda-mental paradigms for designing I/O-efficientalgorithms by using them to design efficientsorting algorithms. We then go on and sur-vey external-memory algorithms for compu-tational geometry problems—with special em-phasis on problems with applications in GIS—and techniques for designing such algorithms:Using the orthogonal line segment intersec-tion problem we illustrate the distribution-sweeping and the buffer tree techniques whichcan be used to solve a large number of im-portant problems. Using the batched rangesearching problem we introduce the exter-nal segment tree. We also discuss an algo-rithm for the reb/blue line segment intersec-tion problem—an important subproblem inmap overlaying. In doing so we introduce

the batched filtering and the external fractionalcascading techniques. Finally, we shortly de-scribe TPIE—a Transparent Parallel I/O En-vironment designed to allow programmers towrite I/O-efficient programs.These lecture notes were made for the CISMAdvanced School on Algorithmic Foundationsof Geographic Information Systems, Septem-ber 16–20, 1996, Udine, Italy.

Contents

1 Introduction

1.1 The Parallel Disk Model1.2 Outline

2 RAM-Complexity and I/O-Complexity

2.1 Fundamental External-MemoryBounds

2.2 Summary

3 Paradigms for Designing I/O-efficientAlgorithms

3.1 Merge Sort3.2 Distribution Sort3.3 Buffer Tree Sort3.4 Sorting on Parallel Disks3.5 Summary

4 External-Memory Computational Geom-etry Algorithms

4.1 The Orthogonal Line Segment Inter-section Problem

4.2 The Batched Range Searching Prob-lem

4.3 The Red/Blue Line Segment Inter-section Problem

4.4 Other External-Memory Computa-tional Geometry Algorithms

4.5 Summary

5 TPIE — A Transparent Parallel I/O Envi-ronment

6 Conclusions.

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BRICS Dissertations Series, 1996 ISSN 1396-7002

4 Torben Brauner. An Axiomatic Approach to Ad-equacy. November 1996. Ph.D. thesis. 168 pp.

3 Lars Arge. Efficient External-Memory DataStructures and Applications. August 1996. Ph.D.thesis. xii+169 pp.

2 Allan Cheng. Reasoning About Concurrent Com-

putational Systems. August 1996. Ph.D. thesis.xiv+229 pp.

1 Urban Engberg. Reasoning in the Temporal Logicof Actions — The design and implementation of aninteractive computer system. August 1996. Ph.D.thesis. xvi+222 pp.

NewsBRICS International PhD School inComputer Science

BRICS now offers an international PhD School inComputer Science at the University of Aarhus.The school provides a PhD programme in com-puter science, and admits 10-12 students annu-ally. It offers a substantial number of grants forDanish as well as foreign students. The school isfunded by the Danish National Research Foun-dation, and institutionally the school is a part ofthe Department of Computer Science at Univer-sity of Aarhus, i.e., it operates within the univer-sity regulations, and all PhD candidates get theirdegree from the University of Aarhus.

The purpose of the PhD School is: to create atruly international graduate school in Denmarkoffering a programme of courses and projectwork of high scientific quality, and to recruitDanish as well as foreign PhD students of thehighest international standards. It providesan excellent research environment and scien-tific training facilities, and aims at making itsPhD graduates attractive for a wide spectrum ofemployers—in private and public research anddevelopment institutions, both in Denmark andabroad.

It is the hope to attract Computer Science stu-dents with four years of full time study andtrained researcher interested in joining the PhDSchool for a shorter or longer period as a teacherand researcher.

The official inauguration of the PhD School tookplace on February 24, 1997, cf. figure 3. The firststudents will be admitted on September 1, 1997.

Admission and PhD Student Grants

The admission requirements for PhD studies incomputer science are knowledge correspondingto four years of full-time study in computer sci-ence at a recognised university. All students willbe admitted to the BRICS PhD School studiesat some level in the four years of PhD studies,transferring previous relevant educational activ-ities.

There will be a number PhD Student Grantsranging from financial aid to tuition waiver andfull studentship.

See the BRICS web pages for further informationand instructions on how to apply.

Tools for Automated Verification ofEmbedded Software – A Collaborationbetween Basic Research and Industry

by Arne Skou

The danish software company Beologic A/S hasrecently initiated a research project in collabo-ration with the section for computer based sys-tems at DTU (Technical University of Denmark)and the concurrency group at BRICS. The collab-oration is supported by the danish Centre for In-

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Figure 3: Inaugural Talk of Mogens Nielsen, director of the new PhD School. In the foreground fromthe left: Peder Olesen Larsen (director of the Danish National Research Foundation), Henning Lehmann(rector of the University of Aarhus) and Ole Vig Jensen (the Danish Minister of Education).

formation Technology (CIT), and it is a primarygoal to support further development of the com-pany’s visualState tool system. This developmentwill be based on recent results from basic re-search – in particular within model checking.

Embedded software is part of almost all mod-ern household equipment and also of advancedequipment for control and monitoring in largeindustrial systems. The complexity of such soft-ware is a prerequisite for the equipment func-tionality, and it is a well recognised fact that thedevelopment of verification tools for embeddedsoftware is an important competitive parame-ter for the equipment suppliers. During recentyears, there has been a minor revolution of suchtools wrt. their functionality and application ar-eas, and it is a necessity that Danish companiesare offered the possibility to exploit this devel-opment. The project will make a contribution toimprove the present market.

A few words about Beologic A/S: The companyis a fast growing software company with a ma-

jor activity on development and marketing ofthe visualState tool for embedded software de-velopment. The product supports design andcode generation of state machines as well as statespace analysis of up to 300 million states. The de-velopment of visualState is based on more than 10years of work on Bang & Olufsen products. Thecompany has more than 50 national costumers(including B&O, Grundfos, Danfoss and TermaElectronics), and it is looking forward to offer-ing improved tool performance based on the re-search project.

Contact persons:

Beologic A/S: Technical Director Niels Bo Theil-gaard, phone +45 4453 8888.

Technical University of Denmark: professorJørgen Staunstrup, phone +45 4525 3740.

BRICS: professor Kim G. Larsen, phone +45 96358080.

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Calendar of Events

Date Event

29–30 Apr Mini-course on Algebraic Theory of Automata, Temporal Logic andExpressiveness

1–2 May Mini-course on Information Theoretic Security in Cryptography

5–6 May Combinatorial Optimisation Meeting

Mid May Mini-course on First Order Logic with Dependent Sorts, Simulation, andHigher Dimensional Categories

20–23 May Mini-course on Inductive Logic Programming

30 Jun – 2 Jul Combinatorial Pattern Matching, CPM ’97

23–29 Aug Computer Science Logic, CSL ’97

BRICS Address and World Wide WebPlease note that the ftp area of the Centre nowcan be accessed directly from the BRICS ftp ad-dress. The old access way, however, will con-tinue to be valid.

For further information, hard copies of informa-tion material and reports of the BRICS Series aswell as enrolment into the BRICS newsgroup,please contact BRICS at

Telephone: +45 8942 3360Telefax: +45 8942 3255Internet: <BRICS@brics.dk>

or, in writing, to

BRICSDepartment of Computer ScienceUniversity of AarhusNy Munkegade, building 540DK - 8000 Aarhus CDenmark.

You can get access to information from BRICSthrough World Wide Web (WWW) and anony-mous FTP. To connect to the BRICS WWW entry,

open the URL:

http://www.brics.dk/

The BRICS WWW entry contains updated infor-mation about most of the topics covered in thenewsletter as well as access to electronic copiesof information material and reports of the BRICSSeries (look under Publications).

To access the information material and reports ofthe BRICS Series via anonymous FTP do the fol-lowing:

ftp ftp.brics.dkget README.

BRICS Newsletter

ISSN 0909-6043

Editors: Glynn Winskel & Uffe H. EngbergLay-out: Uffe H. EngbergPublisher: BRICSPrint: Departments of Mathematical Sciences

University of Aarhusc© BRICS1997

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