Introduction to Computer Theory

This text strikes a good balance between rigor and an intuitive approach to computer theory. Covers all the topics needed by computer scientists with a sometimes humorous approach that reviewers found "refreshing". It is easy to read and the coverage of mathematics is fairly simple so readers do not have to worry about proving theorems.

Daniel Isaac Aryeh Cohen is an American mathematician and computer scientist who is now a professor emeritus at Hunter College.

PART I AUTOMATA THEORY

Background

2

(5)

Languages

7

(14)

Languages in the Abstract

7

(3)

Introduction to Defining Languages

10

(4)

Kleene Closure

14

(5)

Problems

19

(2)

Recursive Definitions

21

(10)

A New Method for Defining Languages

21

(4)

An Important Language: Arithemetic Expressions

25

(3)

Problems

28

(3)

Regular Expressions

31

(21)

Defining Languages by Another New Method

31

(4)

Formal Definition of Regular Expressions

35

(8)

Languages Associated with Regular Expressions

43

(1)

Finite Languages Are Regular

44

(1)

How Hard It Is To Understand a Regular Expression

45

(3)

Introducing EVEN-EVEN

48

(1)

Problems

49

(3)

Finite Automata

52

(24)

Yet Another Method for Defining Languages

52

(7)

FAs and Their Languages

59

(10)

EVEN-EVEN Revisited

69

(2)

Problems

71

(5)

Transition Graphs

76

(16)

Relaxing the Restriction on Inputs

76

(5)

Looking at TGs

81

(5)

Generalized Transition Graphs

86

(1)

Nondeterminism

87

(1)

Problems

88

(4)

Kleene's Theorem

92

(57)

Unification

92

(1)

Turning TGs into Regular Expressions

93

(15)

Converting Regular Expressions into FAs

108

(27)

Nondeterministic Finite Automata

135

(5)

NFAs and Kleene's Theorem

140

(2)

Problems

142

(7)

Finite Automata with Output

149

(20)

Moore Machines

149

(3)

Mealy Machines

152

(4)

Moore = Mealy

156

(5)

Transducers as Models of Sequential Circuits

161

(3)

Problems

164

(5)

Regular Languages

169

(18)

Closure Properties

169

(3)

Complements and Intersections

172

(13)

Problems

185

(2)

Nonregular Languages

187

(20)

The Pumping Lemma

187

(9)

The Myhill--Nerode Theorem

196

(4)

Quotient Languages

200

(3)

Problems

203

(4)

Decidability

207

(17)

Equivalence

207

(7)

Finiteness

214

(3)

Problems

217

(7)

PART II PUSHDOWN AUTOMATA THEORY

Context-Free Grammars

224

(35)

Syntax as a Method for Defining Languages

224

(6)

Symbolism for Generative Grammars

230

(11)

Trees

241

(4)

Lukasiewicz Notation

245

(5)

Ambiguity

250

(2)

The Total Language Tree

252

(2)

Problems

254

(5)

Grammatical Format

259

(30)

Regular Grammars

259

(6)

Killing Λ-Productions

265

(7)

Killing Unit Productions

272

(3)

Chomsky Normal Form

275

(7)

Leftmost Derivations

282

(3)

Problems

285

(4)

Pushdown Automata

289

(29)

A New Format for FAs

289

(4)

Adding a Pushdown Stack

293

(14)

Defining the PDA

307

(5)

Problems

312

(6)

CFG = PDA

318

(33)

Building a PDA for Every CFG

318

(9)

Building a CFG for Every PDA

327

(21)

Problems

348

(3)

Non-Context-Free Languages

351

(25)

Self-Embeddedness

351

(9)

The Pumping Lemma for CFLs

360

(13)

Problems

373

(3)

Context-Free Languages

376

(26)

Closure Properties

376

(9)

Intersection and Complement

385

(8)

Mixing Context-Free and Regular Languages

393

(5)

Problems

398

(4)

Decidability

402

(32)

Emptiness and Uselessness

402

(6)

Finiteness

408

(2)

Membership---The CYK Algorithm

410

(5)

Parsing Simple Arithmetic

415

(14)

Problems

429

(5)

PART III TURING THEORY

Turing Machines

434

(23)

The Turing Machine

434

(15)

The Subprogram INSERT

449

(3)

The Subprogram DELETE

452

(2)

Problems

454

(3)

Post Machines

457

(23)

The Post Machine

457

(5)

Simulating a PM on a TM

462

(6)

Simulating a TM on a PM

468

(9)

Problems

477

(3)

Minsky's Theorem

480

(14)

The Two-Stack PDA

480

(2)

Just Another TM

482

(10)

Problems

492

(2)

Variations on the TM

494

(41)

The Move-in-State Machine

494

(5)

The Stay-Option Machine

499

(3)

The k-Track TM

502

(9)

The Two-Way Infinite Tape Model

511

(7)

The Nondeterministic TM

518

(6)

The Read-Only TM

524

(7)

Problems

531

(4)

TM Languages

535

(30)

Recursively Enumerable Languages

535

(10)

The Encoding of Turing Machines

545

(4)

A Non-Recursively Enumerable Language

549

(3)

The Universal Turing Machine

552

(5)

Not All r.e. Languages Are Recursive

557

(1)

Decidability

558

(4)

Problems

562

(3)

The Chomsky Hierarchy

565

(29)

Phrase-Structure Grammars

565

(9)

Type 0 = TM

574

(12)

The Product and Kleene Closure of r.e. Languages

586

(2)

Context-Sensitive Grammars

588

(2)

Problems

590

(4)

Computers

594

(25)

Defining the Computer

594

(5)

Computable Functions

599

(11)

Church's Thesis

610

(2)

TMs as Language Generators

612

(4)

Problems

616

(3)

Bibliography

619

(2)

Theorem Index

621

(4)

Index

625

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Introduction to Computer Theory

Summary

Author Biography

Table of Contents

Supplemental Materials

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Introduction to Computer Theory

Summary

Author Biography

Table of Contents

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