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'Languages and Machines' covers key concepts and theorems of the theory of computation. The third edition provides a mathematically sound presentation augmented with the theory of computer science. It incorporates step-by-step, unhurried proofs, worked-out examples and illustrations providing students the needed aid in understanding concepts.
The third edition of "Languages and Machines: An Introduction to the Theory of Computer Science "provides readers with a mathematically sound presentation of the theory of computer science. The theoretical concepts and associated mathematics are made accessible by a "learn as you go" approach that develops an intuitive understanding of the concepts through numerous examples and illustrations."
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Thomas A. Sudkamp
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IntroductionPart I: FoundationsChapter 1: Mathematical Preliminaries1.1 Set Theory1.2 Cartesian Product, Relations, and Functions1.3 Equivalence Relations1.4 Countable and Uncountable Sets1.5 Diagonalization and Self-Reference1.6 Recursive Definitions1.7 Mathematical Induction1.8 Directed GraphsExercisesBibliographic NotesChapter 2: Languages2.1 Strings and Languages2.2 Finite Specification of Languages2.3 Regular Sets and Expressions2.4 Regular Expressions and Text SearchingExercisesBibliographic NotesPart II: Grammars, Automata, and LanguagesChapter 3: Context-Free Grammars3.1 Context-Free Grammars and Languages3.2 Examples of Grammars and Languages3.3 Regular Grammars3.4 Verifying Grammars3.5 Leftmost Derivations and Ambiguity3.6 Context-Free Grammars and Programming Language DefinitionExercisesBibliographic NotesChapter 4: Normal Forms for Context-Free Grammars4.1 Grammar Transformations4.2 Elimination of Rules4.3 Elimination of Chain Rules4.4 Useless Symbols4.5 Chomsky Normal Form4.6 The CYK Algorithm4.7 Removal of Direct Left Recursion4.8 Greibach Normal FormExercisesBibliographic NotesChapter 5: Finite Automata5.1 A Finite-State Machine5.2 Deterministic Finite Automata5.3 State Diagrams and Examples5.4 Nondeterministic Finite Automata5.5 Transitions5.6 Removing Nondeterminism5.7 DFA MinimizationExercisesBibliographic NotesChapter 6: Properties of Regular Languages6.1 Finite-State Acceptance of Regular Languages6.2 Expression Graphs6.3 Regular Grammars and Finite Automata6.4 Closure Properties of Regular Languages6.5 A Nonregular Language6.6 The Pumping Lemma for Regular Languages6.7 The Myhill-Nerode TheoremExercisesBibliographic NotesChapter 7: Pushdown Automata and Context-Free Languages7.1 Pushdown Automata7.2 Variations on the PDA Theme7.3 Acceptance of Context-Free Languages7.4 The Pumping Lemma for Context-Free Languages7.5 Closure Properties of Context-Free LanguagesExercisesBibliographic NotesPart III: ComputabilityChapter 8: Turing Machines8.1 The Standard Turing Machine8.2 Turing Machines as Language Acceptors8.3 Alternative Acceptance Criteria8.4 Multitrack Machines8.5 Two-Way Tape Machines8.6 Multitape Machines8.7 Nondeterministic Turing Machines8.8 Turing Machines as Language EnumeratorsExercisesBibliographic NotesChapter 9: Turing Computable Functions9.1 Computation of Functions9.2 Numeric Computation9.3 Sequential Operation of Turing Machines9.4 Composition of Functions9.5 Uncomputable Functions9.6 Toward a Programming LanguageExercisesBibliographic NotesChapter 10: The Chomsky Hierarchy10.1 Unrestricted Grammars10.2 Context-Sensitive Grammars10.3 Linear-Bounded Automata10.4 The Chomsky HierarchyExercisesBibliographic NotesChapter 11: Decision Problems and the Church-Turing Thesis11.1 Representation of Decision Problems11.2 Decision Problems and Recursive Languages11.3 Problem Reduction11.4 The Church-Turing Thesis11.5 A Universal Turing MachineExercisesBibliographic NotesChapter 12: Undecidability12.1 The Halting Problem for Turing Machines12.2 Problem Reduction and Undecidability12.3 Additional Halting Problem Reductions12.4 Rice''s Theorem12.5 An Unsolvable Word Problem12.6 The Post Correspondence Problem12.7 Undecidable Problems in Context-Free GrammarsExercisesBibliographic NotesChapter 13: Mu-Recursive Functions13.1 Primitive Recursive Functions13.2 Some Primitive Recursive Functions13.3 Bounded Operators13.4 Division Functions13.5 G�odel Numbering and Course-of-Values Recursion13.6 Computable Partial Functions13.7 Turing Computability and Mu-Recursive Functions13.8 The Church-Turing Thesis RevisitedExercisesBibliographic NotesPart IV: Computational ComplexityChapter 14: Time Complexity14.1 Measurement of Complexity14.2 Rates of Growth14.3 Time Complexity of a Turing Machine14.4 Complexity and Turing Machine Variations14.5 Linear Speedup14.6 Properties of Time Complexity of Languages14.7 Simulation of Computer ComputationsExercisesBibliographic NotesChapter 15: P, NP, and Cook''s Theorem15.