PREFACE			xiii
ACKNOWLEDGEMENTS			xvii
CREDITS			xix
PART I: INTRODUCTION			1
1	Why Study the Theory of Computation?		2
	1.1	The Shelf Life of Programming Tools	2
	1.2	Applications of the Theory Are Everywhere	5
2	Languages and Strings		8
	2.1	Strings	8
	2.2	Languages	10
		Exercises	19
3	The Big Picture: A Language Hierarchy		21
	3.1	Defining the Task: Language Recognition	21
	3.2	The Power of Encoding	22
	3.3	A Machine-Based Hierarchy of Language Classes	28
	3.4	A Tractability Hierarchy of Language Classes	34
		Exercises	34
4	Computation		36
	4.1	Decision Procedures	36
	4.2	Determinism and Nondeterminism	41
	4.3	Functions on Languages and Programs	48
		Exercises	52
PART II: FINITE STATE MACHINES AND REGULAR LANGUAGES			53
5	Finite State Machines		54
	5.1	Deterministic Finite State Machines	56
	5.2	The Regular Languages	60
	5.3	Designing Deterministic Finite State Machines	63
	5.4	NondeterministicFSMs	66
	5.5	From FSMs to Operational Systems	79
	5.6	Simulators for FSMs*	80
	5.7	Minimizing FSMs *	82
	5.8	A Canonical Form for Regular Languages	94
	5.9	Finite State Transducers *	96
	5.10	Bidirectional Transducers *	98
	5.11	Stochastic Finite Automata: Markov Models and HMMs *	101
	5.12	Finite Automata, Infinite Strings: Büchi Automata *	115
		Exercises	121
6	Regular Expressions		127
	6.1	What is a Regular Expression?	128
	6.2	Kleene's Theorem	133
	6.3	Applications of Regular Expressions	147
	6.4	Manipulating and Simplifying Regular Expressions	149
		Exercises	151
7	Regular Grammars *		155
	7.1	Definition of a Regular Grammar	155
	7.2	Regular Grammars and Regular Languages	157
		Exercises	161
8	Regular and Nonregular Languages		162
	8.1	How Many Regular Languages Are There?	162
	8.2	Showing That a Language Is Regular	163
	8.3	Some Important Closure Properties of Regular Languages	165
	8.4	Showing That a Language is Not Regular	169
	8.5	Exploiting Problem-Specific Knowledge	178
	8.6	Functions on Regular Languages	179
		Exercises	182
9	Algorithms and Decision Procedures for Regular Languages		187
	9.1	Fundamental Decision Procedures	187
	9.2	Summary of Algorithms and Decision Procedures	194
		Exercises	196
10	Summary and References		198
PART III: CONTEXT-FREE LANGUAGES AND PUSHDOWN AUTOMATA			201
11	Context-Free Grammars		203
	11.1	Introduction to Rewrite Systems and Grammars	203
	11.2	Context-Free Grammars and Languages	207
	11.3	Designing Context-Free Grammars	212
	11.4	Simplifying Context-Free Grammars *	212
	11.5	Proving That a Grammar is Correct *	215
	11.6	Derivations and Parse Trees	218
	11.7	Ambiguity	220
	11.8	Normal Forms *	232
	11.9	Island Grammars *	241
	11.10	Stochastic Context-Free Grammars *	243
		Exercises	245
12	Pushdown Automata		249
	12.1	Definition of a (Nondeterministic) PDA	249
	12.2	Deterministic and Nondeterministic PDAs	254
	12.3	Equivalence of Context-Free Grammars and PDAs	260
	12.4	Nondeterminism and Halting	274
	12.5	Alternative Equivalent Definitions of a PDA *	275
	12.6	Alternatives that are Not Equivalent to the PDA *	277
		Exercises	277
13	Context-Free and Noncontext-Free Languages		279
	13.1	Where Do the Context-Free Languages Fit in the Big Picture?	279
	13.2	Showing That a Language is Context-Free	280
	13.3	The Pumping Theorem for Context-Free Languages	281
	13.4	Some Important Closure Properties of the Context-Free Languages	288
	13.5	Deterministic Context-Free Languages *	295
	13.6	Ogden's Lemma *	303
	13.7	Parikh's Theorem *	306
	13.8	Functions on Context-Free Languages *	308
		Exercises	310
14	Algorithms and Decision Procedures for Context-Free Languages		314
	14.1	The Decidable Questions	314
	14.2	The Undecidable Questions	320
	14.3	Summary of Algorithms and Decision Procedures	320
		Exercises	322
15	Context-Free Parsing*		323
	15.1	Lexical Analysis	325
	15.2	Top-Down Parsing	327
	15.3	Bottom-Up Parsing	340
	15.4	Parsing Natural Languages	350
		Exercises	358
16	Summary and References		360
PART IV: TURING MACHINES AND UNDECIDABILITY			363
17	Turing Machines		364
	17.1	Definition, Notation and Examples	364
	17.2	Computing With Turing Machines	375
	17.3	Adding Multiple Tapes and Nondeterminism	382
	17.4	Simulating a “Real” Computer *	393
	17.5	Alternative Turing Machine Definitions	396
	17.6	Encoding Turing Machines as Strings	400
	17.7	The Universal Turing Machine	404
		Exercises	407
18	The Church-Turing Thesis		411
	18.1	The Thesis	411
	18.2	Examples of Equivalent Formalisms *	414
		Exercises	424
19	The Unsolvability of the Halting Problem		426
	19.1	The Language H is Semidecidable but Not Decidable	428
	19.2	Some Implications of the Undecidability of H	431
	19.3	Back to Turing, Church, and the Entscheidungsproblem	432
		Exercises	433
20	Decidable and Semidecidable Languages		435
	20.1	D: The Big Picture	435
	20.2	SD: The Big Picture	435
	20.3	Subset Relationships between D and SD	437
	20.4	The Classes D and SD Under Complement	438
	20.5	Enumerating a Language	440
	20.6	Summary	444
		Exercises	445
21	Decidability and Undecidability Proofs		448
	21.1	Reduction	449
	21.2	Using Reduction to Show that a Language is Not Decidable	452
	21.3	Are All Questions About Turing Machines Undecidable?	466
	21.4	Rice's Theorem *	468
	21.5	Undecidable Questions About Real Programs	472
	21.6	Showing That a Language is Not Semidecidable	474
	21.7	Summary of D, SD/D and ØSD Languages	482
		Exercises	483
22	Decidability of Languages That Do Not (Obviously) Ask Questions about Turing Machines*		487
	22.1	Diophantine Equations and Hilbert's 10th Problem	488
	22.2	Post Correspondence Problem	489
	22.3	Tiling Problems	492
	22.4	Logical Theories	495
	22.5	Undecidable Problems about Context-Free Languages	499
		Exercises	508
23	Unrestricted Grammars*		510
	23.1	Definition and Examples	510
	23.2	Equivalence of Unrestricted Grammars and Turing Machines	516
	23.3	Grammars Compute Functions	518
	23.4	Undecidable Problems About Unrestricted Grammars	521
	23.5	The Word Problem for Semi-Thue Systems	522
		Exercises	524
24	The Chomsky Hierarchy and Beyond*		526
	24.1	The Context-Sensitive Languages	526
	24.2	The Chomsky Hierarchy	539
	24.3	Unification Grammars	540
	24.4	Lindenmayer Systems	544
		Exercises	553
25	Computable Functions*		555
	25.1	What is a Computable Function?	555
	25.2	Recursive Function Theory	565
	25.3	The Recursion Theorem and its Use	573
		Exercises	580
26	Summary and References		581
PART V: COMPLEXITY			585
27	Introduction to the Analysis of Complexity		586
	27.1	The Traveling Salesman Problem	586
	27.2	The Complexity Zoo	589
	27.3	Characterizing Problems	590
	27.4	Measuring Time and Space Complexity	593
	27.5	Growth Rates of Functions	597
	27.6	Asymptotic Dominance	598
	27.7	Algorithmic Gaps	604
	27.8	Examples *	605
		Exercises	617
28	Time Complexity Classes		621
	28.1	The Language Class P	621
	28.2	The Language Class NP	633
	28.3	Does P = NP?	642
	28.4	Using Reduction in Complexity Proofs	644
	28.5	NP-Completeness and the Cook-Levin Theorem	647
	28.6	Other NP-Complete Problems	656
	28.7	The Relationship between P and NP-Complete	672
	28.8	The Language Class Co-NP	679
	28.9	The Time Hierarchy Theorems, EXPTIME, and Beyond	681
	28.10	The Problem Classes FP and FNP	689
		Exercises	690
29	Space Complexity Classes		695
	29.1	Analyzing Space Complexity	695
	29.2	PSPACE, NPSPACE, and Savitch's Theorem	699
	29.3	PSPACE Completeness	704
	29.4	Sublinear Space Complexity	713
	29.5	The Closure of Space Complexity Classes Under Complement	718
	29.6	The Space Hierarchy Theorems	719
		Exercises	720
30	Practical Solutions for Hard Problems		721
	30.1	Approaches	721
	30.2	Randomized Algorithms and the Problem Classes BPP, RP, ZPP	723
	30.3	Heuristic Search	731
		Exercises	740
31	Summary and References		742
APPENDICES			745
A	Review of Mathematical Background: Logic, Sets, Relations, Functions, and Proof Techniques		745
	A.1	Logic	745
	A.2	Sets	753
	A.3	Relations	756
	A.4	Functions	769
	A.5	Closures	776
	A.6	Proof Techniques	779
	A.7	Reasoning about Programs	792
	A.8	A General Definition of Closure *	800
		Exercises	804
B	The Theory: Working with Logical Formulas		808
	B.1	Working with Boolean Formulas	808
	B.2	Working with First-Order Formulas: Clause Form and Resolution	820
	B.3	Exercises	833
C	The Theory: Finite State Machines and Regular Languages		835
D	The Theory: Context-Free Languages and PDAs		839
	D.1	Proof of the Greibach Normal Form Theorem	839
	D.2	Proof that the DCFLs are Closed Under Complement	846
	D.3	Proof of Parikh's Theorem	852
E	The Theory: Turing Machines and Undecidability		856
	E.1	Proof that Nondeterminism Does Not Add Power to Turing Machines	856
	E.2	An Analysis of Iterative Deepening	861
	E.3	The Power of Reduction	862
	E.4	The Undecidability of the Post Correspondence Problem	864
F	The Theory: Complexity		869
	F.1	Asymptotic Dominance	869
	F.2	The Linear Speedup Theorem	875
G	Applications: Programming Languages and Compilers		880
	G.1	Defining the Syntax of Programming Languages	880
	G.2	Are Programming Languages Context-Free?	883
	G.3	Designing Programming Languages and Their Grammars	885
	G.4	Compilers for Programming Languages	887
	G.5	Functional Programming and the Lambda Calculus	890
H	Applications: Tools for Programming, Databases and Software Engineering		899
	H.1	Proving Correctness Properties of Programs and Hardware	899
	H.2	Statecharts: A Technique for Specifying Complex Systems	910
	H.3	Model-Based Test Case Generation	913
	H.4	Reverse Engineering	914
	H.5	Normal Forms for Data and for Querying Relational Data Bases	916
I	Applications: Networks		918
	I.1	Network Protocols	918
	I.2	Modeling Networks as Graphs	927
	I.3	Exploiting Knowledge: The Semantic Web	929
J	Applications: Security		948
	J.1	Physical Security Systems as FSMs	948
	J.2	Computer System Safety	949
	J.3	Cryptography	955
	J.4	Hackers and Viruses	959
K	Applications: Computational Biology		962
	K.1	A (Very) Short Introduction to Molecular Biology and Genetics	962
	K.2	The Sequence Matching Problem	968
	K.3	DNA and Protein Sequence Matching Using the Tools of Regular Languages	970
	K.4	RNA Sequence Matching and Secondary Structure Prediction Using the Tools of Context-Free Languages	975
	K.5	Complexity of the Algorithms Used in Computational Biology	977
L	Applications: Natural Language Processing		978
	L.1	Morphological Analysis	978
	L.2	Part of Speech Tagging	981
	L.3	The Grammar of English	983
	L.4	Building a Complete NL System	998
	L.5	Speech Understanding Systems	999
M	Applications: Artificial Intelligence and Computational Reasoning 1004
	M.1	The Role of Search	1006
	M.2	A Logical Foundation for Artificial Intelligence	1007
	M.3	A Rule-Based Foundation for Artificial Intelligence and Cognition	1022
N	Applications: Entertainment: Music and Games		1028
	N.1	Music 1028
	N.2	Classic Games and Puzzles	1034
	N.3	Interactive Video Games	1046
O	Applications: Using Regular Expressions		1050
P	Using Finite State Machines and Transducers		1054
	P.1	Finite State Machines Predate Computers	1054
	P.2	The Towers of Hanoi: Regular Doesn't Always Mean Tractable	1058
	P.3	The Arithmetic Logic Unit (ALU)	1060
	P.4	Controlling a Soccer-Playing Robot	1062
Q	Applications: Using Grammars		1065
	Q.1	Describing Artificial Languages Designed for Person/Machine Interaction	1066
	Q.2	Describing Naturally Occurring Phenomena	1071
REFERENCES			1073
INDEX			1085