CS 454 Theory of Computation

Sonoma State University, Fall 2012Instructor: B. (Ravi) Ravikumar

Office: 116 I Darwin Hall

Lecture 1

Goals:• overview (45 minutes)• Course overview• Field overview

• Chapter 1 (55 minutes)

What is theory of computation?

Theory of computation deals with computational models – what they can and can’t do.

Computational models: instead of defining it, we will give some examples.

• Cellular automaton

• L-system

• finite automaton

Virtual cities generated using L systems

Course overview

finite automata• DFA, NFA, regular expressions• proof of equivalence, algorithms for conversions• What can’t be done by FA?• DFA minimization

• context-free languages• grammar, pushdown automaton• equivalence• what can’t be done by cfg’s?

• Turing machines• computability• variations of Turing machines• reductions, unsolvability• other computational models

• Complexity Theory• time complexity• NP-completeness

• Other topics• applications (e.g. compilers, image compression, graphics etc.)• cryptography, interactive proof systems• biologically inspired models of computation

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Why Study Theory of Computation? From Stanford survey (Jeff Ullman)

A survey of Stanford grads 5 years out asked which of their courses did they use in their job.

Basics like CS106 (~ CS 215) took the top spots, of course.

But among optional courses, CS 154 stood remarkably high.3X the score for AI, for example.

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How Could That Be?

Regular expressions are used in many systems.E.g., UNIX a.*b.E.g., DTD's (Document Type Definition)

describe XML tags with a RE format like person (name, addr, child*).

Finite automata model protocols, electronic circuits.Theory is used in model-checking.

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How? – (2)

Context-free grammars are used to describe the syntax of essentially every programming language.Not to forget their important role in

describing natural languages. And DTD’s taken as a whole, are

really CFG’s.

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How? – (3)

When developing solutions to real problems, we often confront the limitations of what software can do.Undecidable things – no program

whatever can do it.Intractable things – there are programs,

but no fast programs.CS 454 (and CS 415) give you the

tools.

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Other aspects of CS 454

We’ll learn how to deal formally with discrete systems.Proofs: You never really prove a program correct,

but you need to be thinking of why a tricky technique really works.

Abstract models are important to design and understand complex software. Abstract State Machine used to design Microsoft

productsState Charts play a key role in software systems.

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Text

Hopcroft, Motwani, Ullman, Automata Theory, Languages, and Computation 3rd Edition.

Goal is to cover roughly ¾ of the book.

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Gradiance Registration

The “class token” for this edition of CS 454 is 7AC0798E

Register it at www.gradiance.com

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Homework

The intent is that everyone will get 100% on all homeworks.

You are allowed to try as many times as you like.Only the last try counts.

Don’t be afraid to guess and try again.

You’ll get some advice if you make a mistake.