Relational algebraic system entity structure for models management

H.C. Park T.G. Kim

Indexing terms: Models management, Relational algebra, Relational database

Abstract: Models management with a large number of models has placed demands on a highly structured and rigorous framework. The paper proposes a new framework, callcd RASES, that is based on the system entity structure (SES) formalism and the relational algebra (RA) formalism. These formalisms provide conceptual bases for the hierarchical management of models. Within the RASES framework, the hierarchical structures of models are represented in the form of entity structure that may be stored as relational tables in a database. Furthermore, several operations can be formulated in terms of relational algebra which can be coded in a standard query language such as the SQL. The RASES framework can be easily implemented on, and fully utilise the functionality of, the relational database management system (RDBMS). Huge amount of models and model structures, which is inevitable in the models management of real world systems, can be efficiently managed by virtue of the capability of RDBMS. The framework supports modellers to synthesise simulation models that meet their modelling objectives, and conduct appropriate experiments on the models under investigation.

1 Introduction

The modelling of complex systems and the models management with a large number of models have placed demands on highly structured and rigorous framework [I]. To control the complexity of the model- ling and models management, the structural knowledge of models must be separately managed from the behav- iour of the models. Furthermore, the models must be specified in a modular form so that a composite model can be constructed just by coupling input/output ports of the models [2]. The composite model may itself be in a modular form and therefore employed as a compo- nent to be coupled together with other components to build yet more complex, hierarchical models. The hier- 0 IEE, 1996 IEE Proceedings online no. 19960166 Paper first received 1st August 1994 and in final revised form 7th April 1995 The authors are with the Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, 373-1 Kusong-Dong, Yusong-Ku, Taejon 305-701, Korea

archical structure of such a model is termed as model structure. The models management problem focused in this paper concerns how to manage models in a library of models, how to organise a family of model struc- tures in a unified form, and how to construct new mod- els from existing models and model structures.

It is natural to think that some kinds of computer based framework may be devised to support the models management for improving the productivity of model- lers. This paper proposes a new framework, called rela- tional algebraic system entity structure (RASES), to cope with the models management problem. It is based on the system entity structure (SES) formalism [2-6] and the relational algebra (RA) formalism [7].

Fig. 1 shows the fundamental concept of the models management within the RASES framework. Here an entity structure serves as a means of organising a fam- ily of model structures. A pruned entity structure can be extracted from the entity structure and synthesised into a simulation model. The entity structure itself is formulated in terms of relational tables under the RA formalism. Furthermore, several operations, such as the pruning operation, can be defined in the relational algebra. Accordingly, the RASES framework provides an integrated approach within which one may system- atically manage simulation models.

rMode' Bas- e (p+i$&+

i t

Pruned

4 r E n t i t y Structur

'I-" I I LIFO PROC I I

1 Model Synthesis Concept of models management Fig. 1

The RASES framework can exploit the power of relational database. Relational database has been applied successfully to several applications such as a protocol verification [8], and accepted as a method to overcome limits of traditional approaches. It has been an effective method for managing large amounts of data, sharing data among users, and fast queries. The well defined query languages such as the SQL [9] can be used to manipulate the databases. In the models management problem, there may be a large number of models and model structures which must be stored to provide sharable repository for many modellers. This problem can be alleviated by the database approach because relational database management system

49 IEE Proc-Comput. Digit. Tech., Vol. 143, No. I , January 1996

(RDBMS) provides rich facilities to efficiently manage large amounts of data. Furthermore many models management functions, such as create, delete, and update, are equivalent to database management func- tions. As a consequence, RDBMS is an attractive plat- form for implementing the RASES framework for the models management.

In the work described, the RASES framework has been implemented on a general purpose RDBMS, INFORMIX. Using the framework, modellers can syn- thesise simulation models that meet their modelling objectives, and conduct appropriate experiments on the models under investigation. Furthermore, the frame- work is sufficiently general enough that it can be extended to manage the knowledge of other domains and to serve somewhat different needs of users.

2 SES: system entity structure

2.7 Brief review of SES We review some fundamental concepts of SES that are discussed in greater detail elsewhere [2]. The SES for- malism, proposed by Zeigler, is a structural knowledge representation scheme which systematically organises a family of possible structures of a system. Such a family characterises decomposition, coupling, and taxonomic relationships among entities. The entity represents a real-world object. The decomposition concerns how an entity may be broken down into subentities, and the concept of coupling is to specify how these subentities may be combined to reconstitute the entity. The taxo- nomic relationship concerns admissible variants of an entity.

I- - - - - - - - - - - * D1 1 . ~ 9 )

1 ........................................... ' D2 (-VI 1) GI j-vl21 ,G2 I - N O 1

.............................

Fig. 2 Example of entity structure

As shown in Fig. 2, an entity structure is represented as a labeled tree with attached attributes which satisfies the following axioms: uniformity, strict hierarchy, alter- nating mode, valid brother, and attached variables. Details of the axioms can be found in [2]. There are three types of nodes in the tree. Entity node, like A in Fig. 2, represents a real world object. There are two types of entity, namely composite entity and atomic entity. Composite entity is defined in terms of other entities (which may be either atomic or composite), while atomic entity cannot be broken down into suben- tities. Each entity may be attached with and character- ised by, variables. It may have several aspects and/or specialisations. Aspect node, like A-dec in Fig. 2, is connected by a single vertical line from an entity. It represents one decomposition of the entity. The chil- dren of the aspect are entities, distinct components of the decomposition. Associated with each aspect are coupling specifications. Specialisation node, like B-spec in Fig. 2, is connected by a double vertical line from an

50

entity. It defines the taxonomy of the entity, and repre- sents the way in which the entity can be categorised into specialised entities. Selection rules may be associ- ated with a specialisation, and guide the way in which each specialised entity is selected in the pruning proc- ess. Selection constraint depicted as dashed arrows from an entity to other entities in Fig. 2, means that not all specialised entities may be selected independently [ 101. Once a specialised entity is selected from a specialisa- tion some other specialised entities are also selected from other specialisations associated with the speciali- sation.

Since Zeigler proposed the concepts of SES, there has been a considerable amount of work to make SES more concrete knowledge representation scheme [3, 4, 6, 101 and to accept SES as a conceptual basis for their applications [5, 11, 121.

2.2 Formal definition o f SES SES can be newly formalised by items, relationships among them, attributes attached to them, and selection constraints as follows. Dej5nition I : System Entity Structure (SES) is defined by a 4-tuple: SES = <ITEM, REL, A T T , G s e b ITEM = E v A v S: set of items E : set of entities, A : set of aspects, S : set of specialisations R E L = Asp U Spec : set of relationships among items Asp c E x A x 2E : aspect relationship, Spec c E x S x 2E : specialisation relationship; ATT = Evar U Acoup v Ssel : set of attributes attached to items Evar : E + 2v : variables attached to entities, Acoup : A -+ 2@1° E1O) : couplings attached to aspects, Ssel : S + 2R : selection rules attached to specialisa- tions; GseI : (S x E ) + 2(s where V represents a set of variables, IO represents a set of inputloutput ports of respective entities, and R is a set of selection rules in the form of (cond + E ) . Items (ITEM) are depicted as nodes in the treelike rep- resentation. It is composed of entities (E), aspects (A), and specialisations (S). Relationships (REL) among items define how each item is related with each others and are depicted as edges in the treelike representation. Aspect relationship (Asp) relates each entity with sub- entities through an aspect, and specialisation relation- ship (Spec) relates each entity with specialised entities through a specialisation. Each item may be augmented by attached attributes (ATT). Variables (Evar) are attached to, and characterise, each entity. Couplings (Acoup) are attached to each aspect and can be described in terms of entities with their inputloutput ports. Selection rules (Ssel) are also attached to each specialisation and help the selection process of the pruning. We also consider global selection constraints (Gsel) among specialisations and their specialised enti- ties.

9 : global selection constraints.

IEE Proc -Comput. Digit. Tech., Vol. 143, No. I , JanuaTy 1996

3 structure

RASES: relational algebraic system entity

‘ H D1 D2 G1

This section first briefly reviews the concepts of rela- tion and relational algebra. Then RASES is defined in terms of relations, and a pruning algorithm on RASES is proposed by using relational algebra.

3. I Relational algebra in brief The Cartesian product of domains D1, ..., D,, written Dl x ... x D,, is a set of n-tuples <vl, ..., v,> such that v1 is in D1, v2 is in D2, and so on. Relation is any subset of the Cartesian product of one or more domains and each element of the relation is called tuple. Relation can be represented as a table where each row is tuple and each column has a distinct name called attribute. Each attribute has an associated domain. A relation R with a set of attributes A = { A , , ..., A,} is denoted by R[A] or R [ A , ... A,]. Let t be a tuple in R[A] . Then the part of t corresponding to a set of attributes X E A is denoted by t [ q . The relation name itself is also used to indicate all attributes of the relation, for example t[R].

There is a family of operations usually associated with relations. They can be coded by using algebraic notations, called relational algebra. Fundmental opera- tions in relational algebra are union (U), difference (-), Cartesian product (x), projection (n), and selection (0). In addition to the five fundmental operations there are some other useful operations that can be defined in terms of the operations. They are intersection (n), natu- ral join (W), and theta join (We). Details of such operations can be found in [7]. In addition, we defined a new operation called replacement (0) which is used intensively in a pruning algorithm. Definition 2: Replacement ( @ A PZBP) operation is defined as follows. Let R [ q , S[yl, and R’[Y be rela- tions, and A , , A2 E X and B,, B2 E Y be attributes. Then each tuple r‘ E R’ for R’ = R @ A ~ ~ Z B ~ % S is obtained as follows. For each tuple r E R, if there exists a tuple s E S such that r[Al] = s[Bl] then r’[X - A2] = r[X - A21 and r’[A2] = s[B2] else r’ = r . That is, a replacement operation of R O ( A P Z B ~ ) S means that each value of attribute A2 is replaced with the value of attribute B2 if the condition Al = B, is sat- isfied. The replacement operation can also be coded by using other operations as follows. Here, 8A2 ,+ B2 means that attribute name B2 is changed into A2.

-42+=B2 R @ A ~ = B ~ s = S A z t B 2 ( n E 2 , X - A 2 ( R WA1=B1 s)) U ( R - ~ x ( R W A ~ = B ~ s))

3.2 Definition of RASES Although SES has been visually represented as a tree- like structure it can be transformed into other forms that can coherently convey the information it bears [6]. We propose RASES, a relational formalisation of SES. RASES can be easily defined with relations. Each rela- tion is defined in terms of relation name, attribute names, and some kind of constraints. Dejkition 3: Relational algebraic system entity struc- ture (RASES) is defined by a 6-tuple: RASES = <ASP, SPEC, EVAR, ACOUP, SSEL, GSEL> (i) ASP [ent, asp, subent] : contains aspect relationships among entities. ent is an entity, asp is an aspect, and

IEE Proc -Camput Digtt Tech, Val 143, No I , January 1996

v10 v9 v l l v12

subent is a subentity of the entity ent. This means that the subent is a subentity of ent under the aspect asp. (ii) SPEC [ent, spec, specent] : contains specialisation relationships among entities. ent is an entity, spec is a specialisation, and specent is a specialised entity of the entity ent. This means that specent is a specialised entity of the parent entity ent under the specialisation spec. (iii) EVAR [ent, variable, value] : contains variables attached to entities. ent is an entity to which the varia- ble is attached, and value is the value of the variable. This means that variable, whose value is value, is attached to the entity ent. (iv) ACOUP [asp, entl , portl , e n d , port21 : contains couplings attached to aspects. asp is an aspect, entl is an entity, portl is a port of the entity entl, ent2 is another entity, and port2 is a port of the entity ent2. This means that portl of the entity entl is connected to port2 of the entity ent2 for the aspect asp. (v) SSEL [spec, cond, specent] : contains selection rules attached to specialisations. spec is a specialisation, cond is a condition, and specent is a specialised entity. This means that if the condition cond is satisfied then spe- cent is selected for the specialisation spec. (vi) GSEL [specl, specent I , spec2, specent21 : contains global selection constraints. specl and spec2 are spe- cialisations, specentl is a specialised entity of specl, and specend is a specialised entity of spec2. This means that if specentl is selected from the specialisation specl then specent2 must be selected from the specialisation spec2.

All the relations of RASES are independent of entity structures to be represented. Thus creating an entity structure is a matter of entering data into predefined relations rather than a matter of defining new relations. Furthermore, since all the entity structures built in RASES look alike, they are easier to understand, to combine, and to interchange. Fig. 3 shows the rela- tional tables representation of the example entity struc- ture depicted in Fig. 2.

Fig. 3

ACOUP !asp- _cntl I port1 - e n t ~ port

l A-dec A in I B in IA-dec A in 1C in I A-dec 1 B A-dec C

,B-dec B IB-dec ~ D iB-dec ’ E ‘C-decl I C 1 C-decl 1 B ~C-decl 1 G C-dec21 C

IC-dec2 H I C-decd ~p I

out out

out

’ in out

out out

A out A out

ID In

c out

I

- ASP

A IA-dec B

B-spec B1 ICs& ( G I l D - y e c l D 2 ~- --p I GIspec lG2

Relational tables representation

51

A set of operations has been defined on RASES. These operations allow users to add new items to the relational tables, delete existing items, create and remove relationships among items, and retrieve items and relationships. These operations may be defined in relational algebra. The relational algebra, in turn, can be easily coded in a standard query language such as the SQL.

A-dec A lB1 v3 A-dec BI

A-dec C

B1 v2

B1 v5

3.3 Relational algebraic pruning An entity structure specifies a family of model struc- tures in which every entity is organised by aspects and specialisations. An operation called pruning is to extract a pruned entity structure from the entity struc- ture. Pruned entity structure (PES) is a system entity structure (SES) which has the following restrictions: every nonleaf entity has single aspect, every leaf entity has no aspect, and every entity has no specialisation. The aspect of nonleaf entity represents the unique decomposition of the entity. Pruning process is mainly composed of two parts. First, one aspect and/or one specialised entity is selected from the alternatives hang- ing from each entity. Next, each specialised entity inherits all (substructures, variables, couplings) of its parent entity.

We propose a relational algebraic algorithm of the pruning process as shown in Fig. 4. Stepl selects only one aspect and/or one specialised entity from the alter- natives hanging from each nonleaf entity. Note that an entity may have several aspects and/or specialised enti- ties. In step2, each specialised entity selected in stepl replaces its parent entity on the aspect table. In this way, the specialised entity inherits the substructure of its parent entity. In step3, coupling specifications of each aspect is appropriately modified by replacing each entity in the couplings with its corresponding special- ised entity. In step4, each entity attached with variables is also replaced with its specialised entity. In this way, the specialised entity inherits the variables of its parent entity. Algorithm: Prune

input: ES <ASP, SPEC, EVAR, ACOUP>

Output: PES <ASPpruned, EVARpruned, ACOUPpruned>

Begin

s t e p l : Prune.Select(ES);

s t e p 2 : ASPpruned - (ASPsel G ~ ~ ~ : : ~ ~ : ! ~ " " ' SPEC sel) O:~:~~~~ce"' SPECsel:

s t e p 9 ACOUPsel - aacoup(ACOUP W,.p=orp ASPsel),

ACOUPpruned - (ACOUPsel G~~~~~~:~ce"' SPECsel) G~:~~~~:~ce"' SPEC sei.

s l e p 4 : EVARsel - =EVAR(EVAR Weni=EntVenf=aubml ASPsel) U

~ E V ~ E V A R W e n t = r n t ~ e n t = r p e c . n r SPECsel). EVARpruned - EVAhel O : ~ ~ ~ : ! ~ n f SPEC Eel,

Relational algebraic pruning algorithm End

Fig. 4

in I C in

out , A out out A out

The algorithm in Fig. 5 is to select one aspect and/or one specialised entity for each entity. Stepl selects one aspect from the alternatives hanging from a given entity. Step2 is to select one specialised entity from the alternatives hanging from the entity. If there is only one item to be selected then it is selected automatically. In step3, the selection process proceeds into the next entity in a breadth-first traverse. The selection rules and global selection constraints can also be incorpo- rated into this selection process with some additional work.

An example clarifies the operations of the pruning algorithm described above. Fig. 6 depicts one possible

52

c v4 IB-dec ' D 1 l v 7 B-dec D1 / v 9 ~ B-dec

1G1 f v 8 C-decl ,G1 / v 1 2 1 C-decl

pruned entity structure extracted from the example entity structure in Fig. 2. In the pruning process, the first item from the alternatives is selected and the glo- bal selection constraints are also considered. Fig. 7 shows relational tables representation of the pruned entity structure.

Algorithm: PruneBelect

Input ES <ASP, SPEC> Ozlput. Selection <ASPsel, SPECsel>

Begin NEXT c {root(ES)]; do until NEXT = 0

N c "(NEXT); s l e p l : As - a,,,(r,,t=,v(ASP));

A c select(As);

ASPa - u,,*=N,,,,=A(ASP); ASPsel e ASPsel U ASPa;

stepd. Ss - =spccnt(~enr=~(SPEC)): s t seleet(Ss);

SPECS - u,",=N,.,.,.,~=~(SPEC); SPECsel - SPECsel U SPECS;

depL NEXT e NEXT U a,,aani(ASPa) U

s,pecenf(SPECs) - c N , .

End

Fig. 5 Selection algorithm

BI in D1 in DI out E in E out BI out C , in BI in BI out GI ' i n

A I-vll I ( ( A h . BI in)

(A.in, C.in) A-dec (Bl.out. A.out)

(C.out, A.out))

I I I(B1.i". D1.i") I ((C.in, BI.~")

B1 I-v2,-v3,-v51 c (-v41

&de= @ h u t , E.in) c.decl (Bl.Out, G1.m) , , (G;.out. Cout)) , I (ET BI our)]

E BI G1 (-vS,-v12}

D1 (-v7.-v9)

Fig. 6 Pruned entity structure, tree representation

' A ,A-dec I C 1 / B 1 !B-dec 1 D1 B1 /B-dec E , C IC-decli B1 C C-decll GI

~ .-

Fig. 7 Pruned entity structure, relational tables

4 Implementation of RASES framework

We have implemented the RASES framework as shown in Fig. 8 on a commercially available general purpose RDBMS, INFORMIX. The RDBMS provides rich facilities that can be used to implement applications including the RASES framework. The implementation relies on the ESQLIC, in which the query language SQL is embedded into the host programming language C. The ESQLIC provides all the functionalities of the SQL and C. It allows one to perform computations by using C language on the results of SQL queries. The framework may provide a supporting tool to systemati- cally organise a family of model structures in the form of entity structure according to the principles of

IEE Proc -Comput Digit Tech, Vol 143, No I , January I996

RASES. It also provides a guiding tool to extract a specific model structure from the entity structure by the pruning process.

User I

TRANSD.in)J

1 User lnterface

(CACHE_WB.pmc. PROC-FPU 10)

IMEM.ro,BUS 10) . I

&&+=J Base Base Base

Fig.8 RASESframework

The framework’s core is the databases. SES base and PES base contains entity structures and pruned entity structures, respectively. Model base contains behav- ioural definitions of models each of which may be atomic or composite. Several management modules are built on top of the databases. SES manager module provides several facilities such as construction and modification of entity structures. Pruner module is an implementation of the algebraic pruning algorithm. Model synthesisev module is to synthesise simulation models by combining pruned entity structures with models in the model base. Leaf entities of pruned entity structures are replaced with atomic models, and higher level entities are mapped to composite models by cou- pling the lower-level models.

There are two ways to access the databases. The SQL is a conventional way to access the databases and to exploit the power of database. But the user interface provided by the framework is a quite convenient way to access the databases.

5 Example: computer system

We used a simple computer system as an example whose entity structure is shown in Fig. 9. Although the example may be relatively simple it can present the applicability of the RASES framework to the models management. In the example, we assume that atomic models are already coded and stored in the model base. From these models, a configuration expert can con- struct an entity structure which organises model struc- tures of the computer system. The RASES framework, of course, provides rich facilities which support users to construct this kind of entity structure. As shown in the Figure, the entity structure (COM-EXP) is mainly composed of experimental frame (EF) and computer system (COM). The experimental frame is to experi- ment simulation models of the computer system via simulation studies. It is composed of generator (GENR) to generate inputs to the simulations and transducer (TRANSD) to collect results from the simu- lations. The computer system is specialised into one with no cache (COMNCACHE) and another with a cache (COM-CACHE). The computer system with no cache is decomposed into four components of clock (CLK), processor (PROC), bus (BUS), and memory (MEM). The computer system with a cache is also

IEE Proc-Comput. Digit. Tech., Vol. 143, No I , January 1996

decomposed into same components, but with an addi- tional cache (CACHE). The cache is specialised into write back (CACHEWB) and write through (CACHE-WT) according to the write policies. Other entities are constructed similarly.

COM-EXP I 1 I c o m y d e c I

EF COM I II

GENR A TRANSD COM-NCACHE -CACHE I

I I com-c~he-decI , II I , ;““ncyh;dec , x HGENR LGENR CLK PROC BUS MEM CLK PROC BUS CACHE MEM

I /I

‘c“;l““ mem-dec

ll

CACHE-WB CACHE-WT & I -

PROC-NFPU PROC-FPU ROM RAM

ALU REG ALU FPU REG I Fig.9 Entity structure of computer system

I COM EXP I ((EF.resul~.COM_EXP.rrsulO

exp&c (EF oul. COM-CACHE in) I ICOM-CACHE out. EF in))

I I

Fig. 10 Pruned entity structure of computer system

I I i

Fig. 11 Block diugrum of synthesised model

Once the entity structure has been constructed, mod- ellers can first prune it to extract pruned entity struc- tures according to their modelling objectives. Fig. 10 shows one such pruned entity structure in which COM-CACHE, CACHEWB, and PROC-FPU are selected from the alternatives. The pruned entity struc- ture is then synthesised into a simulation model as shown in Fig. 11 by combining it with the atomic mod- els in the model base. The modellers can finally con- duct appropriate experiments on the simulation model

53

under investigation. The synthesised model may itself be saved into the model base and in turn could be reused as a component to construct more complex models.

6 Conclusions

This paper proposed a new framework, called RASES, to cope with the complexity of models management problem. The RASES framework described here is based on the concepts of system entity structure and relational algebra. The framework is a significant advance, we hope, in the effort to provide computer- based support for the modelling and models manage- ment problem.

We have implemented the RASES framework on a kind of RDBMS, INFORMIX. It is intended to sup- port the work of managing large amounts of models and model structures by providing flexible and rapid access to the databases. We are currently experimenting with complex models and gradually adding features to the framework as needed. Although this paper focused more on the models management, the framework with further research can be applied to other domains if the domain knowledge can be represented in the form of entity structure.

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WIDMAN, L.E., LO

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CODD, E.F.: ‘A relational model of data for large shared data banks’, Comm. ACM, 1970, 13, (6), pp. 377-387 LEE, T.T., and LAI, M.Y.: ‘A relational algebraic approach to protocol verification’, IEEE Trans., 1988, SC14, (2), pp. 184-193 DATE, C.J.: ‘A guide to the SQL standard’ (Addison-Wesley, 1989)

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