Introduction to Computer Theory,9780471137726

Introduction to Computer Theory

by
Edition: 2nd
ISBN13: 9780471137726
ISBN10: 0471137723
Format: Paperback
Pub. Date: 1996-10-25
Publisher(s): Wiley
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Summary

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.

Author Biography

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

Table of Contents

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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