School of Computing 1 Course Overview Changing Perspectives across the course Ganesh Gopalakrishnan...

School of Computing 1

Course OverviewChanging Perspectives across the

course

Ganesh Gopalakrishnan

CS 3100, Fall 2010

School of Computing

University of Utah

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CS 3100 Learning Objectives

Reinforce discrete math

Understand state machines

You will use these ideas in writing formal documentation for yoursoftware / hardware designs in the field

Example : UML state diagrams for vending machines

Example : The structure of inputs taken by a tool you design

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CS 3100 Learning Objectives

Understand more complex computational structures

Example : what happens if we have one stack

Understand how Machines and Textual representations can denoteLanguages

Example : RE and NFA / DFA

Understand when non-determinism becomes ESSENTIALExample :

THERE IS NO DPDA FOR { W W^R | W in sigma* }There is no deterministic parsing scheme for

this language

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Largely, things were about patterns

|| ||| || ||| || ||| || ….

We studied that sometimes delicately specified patterns disappearwhen blended with “white noise”

Example : { (^j )^j | j >= 0 } has CONTEXT-FREE patterns

This pattern is destroyed if you UNION this language with

(* )*

OR Worse still, { ( , ) } ^ *

Much like Mozart can be drowned by Cacophony !

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How far can we carry these “tricks” forward ?Can we define the notion of THE MOST POWERFUL COMPUTER ON EARTH?

(According to who? To Baby Huey? To Clifford? … Fred Flintston? )

Can we define the ULTIMATE COMPUTER?

No other computational approach can be more powerful?

That space / time / memory are arbitrary quantities?

What is “screaming fast” may not be so in 10 years?

Recall : in 1993, Pentium-2 clocked at a “screaming” 68 MHz

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On Computation

Ganesh Gopalakrishnan

CS 3100, Fall 2010

School of Computing

University of Utah

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Why Compute?

Tool usage is a measure of intelligence and power

Information processing tools have, historically, been widely sought

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Info. processing helped calculate artillery ranges!

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Early Info. Processing Tools were Clunky and Big! (e.g. Babbage’s Difference Engine, now rebuilt at the London Museum)

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With Advances in Electronics have come Faster Computing Devices!

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These Computers are now Everywhere!

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They will soon replace bar-codes on milk-cans!(RFID tags being experimented by Wal-mart).

(Photo courtesy of wikipedia.)

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Supercomputers have eliminated the need to do experiments by building scale models of airplanes, or mixing (dangerous) chemicals !

IBM BlueGene

Does 400 Trillion

multiplications per second !

(Photo courtesy of IBM.)

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Virtual Roll-out of Boeing 787 “Dreamliner”

Entire Airplane beingDesigned and Flown inside a Computer (Simulation Program).

The first plane to fly isthe real one (not a mockup model).

(Photo courtesy of Boeing.)

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Such supercomputers can now safely simulate explosions !

This simulation employed 600 processors for approximately 1 week in a  sophisticated parallel application to simulate all of the fluid  dynamics, thermodynamics, chemical reactions and structural mechanics of this system from fundamental laws of physics.

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* How do we understand various manifestations of computation in a unified manner?* How do we study the essential properties of computing devices?

We want approaches that allow us to separate the Essential from the Accidental

> Computers are changing in design details

> They were growing predictably fast for several decades

> Their I/O modalities keep changing (punched card, command line, point and click, gesture)

> Forgetting all these Accidental aspects, what Essential properties are true for ALL computing devices?

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* How do we understand various manifestations of computation in a unified manner?

* How do we study the essential properties of computing devices?

Answer : * build abstract machines devoid of “sundry details”Conundrum: * Several such formal models (abstract machines) have been proposed

Fundamental Result (“Church’s Thesis”): All these models are equivalent!

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Alonzo Church : 1903 - 1995

http://en.wikipedia.org/wiki/Alonzo_Church

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Alan Turing’s model (“Turing Machine”) was formulated in the 1930s [Turing, 1912 – tragically 1954]

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Gordon Brown’s Apology:

PM's apology to codebreaker Alan Turing: we were inhumane

• Enigma genius chemically castrated for being gay• Admission comes 55 years after Turing took his life

http://www.guardian.co.uk/world/2009/sep/11/pm-apology-to-alan-turing

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Interesting factoid: Church was Turing’s PhD advisor (well, Turing had done most of his work, then went to Princeton to “officially earn a PhD”)

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First, let us see the full taxonomy of computational devices

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Models of computation proposed by Church and Turing:

LambdaLambdaLambda…

Naw Naw NawJolly good advisor,It is TAPE, HEAD, Halt, Loop

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Universality of Lambda Calculus

S and K are universal !!

S = L x y z . x z (y z)

K = L x y . x

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Two-counter machines are universal

Two infinite-precision integer countersare enough to express ALL computations

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Two Stacks (plus finite control) are enough

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Two infinite stacks are like one infinite tape …

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A Single-Instruction RISC Computer

subleq a, b, c ; Mem[b] = Mem[b] - Mem[a] ; if (Mem[b] ≤ 0) goto c

http://en.wikipedia.org/wiki/One_instruction_set_computer

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All these are Turing Complete!

Church Complete,Darn It !!

Har Har Har !

Go Touring !! Take a walk !!