Book:John E. Hopcroft/Introduction to Automata Theory, Languages, and Computation

Affectionately known as "The Cinderella Book".

Subject Matter

 * Computer Science

Contents

 * Preface


 * Chapter 1 Preliminaries
 * 1.1 Strings, alphabets and languages
 * 1.2 Graphs and trees
 * 1.3 Inductive proofs
 * 1.4 Set notation
 * 1.5 Relations
 * 1.6 Synopsis of the book


 * Chapter 2 Finite Automata and Regular Expressions
 * 2.1 Finite state systems
 * 2.2 Basic definitions
 * 2.3 Nondeterministic finite automata
 * 2.4 Finite automata with $\epsilon$-moves
 * 2.5 Regular expressions
 * 2.6 Two-way finite automata
 * 2.7 Finite automata with output
 * 2.8 Applications of finite automata


 * Chapter 3 Properties of Regular Sets
 * 3.1 The pumping lemma for regular sets
 * 3.2 Closure properties of regular sets
 * 3.3 Decision algorithms for regular sets
 * 3.4 The Myhill-Nerode theorem and minimization of finite automata


 * Chapter 4 Context-Free Grammars
 * 4.1 Motivation and introduction
 * 4.2 Context-free grammars
 * 4.3 Derivation trees
 * 4.4 Simplification of context-free grammars
 * 4.5 Chomsky's normal form
 * 4.6 Greibach normal form
 * 4.7 The existence of inherently ambiguous context-free languages


 * Chapter 5 Pushdown Automata
 * 5.1 Informal description
 * 5.2 Definitions
 * 5.3 Pushdown automata and context-free languages


 * Chapter 6 Properties of Context-Free Languages
 * 6.1 The pumping lemma for CFL's
 * 6.2 Closure properties of CFL's
 * 6.3 Decision algorithms for CFL's


 * Chapter 7 Turing Machines
 * 7.1 Introduction
 * 7.2 The Turing machine model
 * 7.3 Computable languages and functions
 * 7.4 Techniques for Turing machine construction
 * 7.5 Modifications of Turing machines
 * 7.6 Church's hypothesis
 * 7.7 Turing machines as enumerators
 * 7.8 Restricted Turing machines equivalent to the basic model


 * Chapter 8 Undecidability
 * 8.1 Problems
 * 8.2 Properties of recursive and recursively enumerable languages
 * 8.3 Universal Turing machines and an undecidable problem
 * 8.4 Rice's theorem and some more undecidable problems
 * 8.5 Undecidability of Post's correspondence problem
 * 8.6 Valid and invalid computations of TM's: a tool for proving CFL problems undecidable
 * 8.7 Greibach's theorem
 * 8.8 Introduction to recursive function theory
 * 8.9 Oracle computations


 * Chapter 9 The Chomsky Hierarchy
 * 9.1 Regular grammars
 * 9.2 Unrestricted grammars
 * 9.3 Context-sensitive languages
 * 9.4 Relations between classes of languages


 * Chapter 10 Deterministic Context-Free Languages
 * 10.1 Normal forms for DPDA's
 * 10.2 Closure of DCFL's under complementation
 * 10.3 Predicting machines
 * 10.4 Additional closure properties of DCFL's
 * 10.5 Decision properties of DCFL's
 * 10.6 $\map {LR} 0$ grammars
 * 10.7 $\map {LR} 0$ grammars and DPDA's
 * 10.8 $\map {LR} k$ grammars


 * Chapter 11 Closure Properties of Families of Languages
 * 11.1 Trios and full trios
 * 11.2 Generalized sequential machine mappings
 * 11.3 Other closure properties of trios
 * 11.4 Abstract families of languages
 * 11.5 Independence of the AFL operations
 * 11.6 Summary


 * Chapter 12 Computational Complexity Theory
 * 12.1 Definitions
 * 12.2 Linear speed-ups, tape compression and reductions in the number of tapes
 * 12.3 Hierarchy theorems
 * 12.4 Relations among complexity measures
 * 12.5 Translation lemmas and nondeterministic hierarchies
 * 12.6 Properties of general complexity measures: the gap, speedup, and union theorems
 * 12.7 Axiomatic complexity theory


 * Chapter 13 Intractable Problems
 * 13.1 Polynomial time and space
 * 13.2 Some $NP$-complete problems
 * 13.3 The class co-$\mathscr {NP}$
 * 13.4 PSPACE-complete problems
 * 13.5 Complete problems for $\mathscr P$ and $\map {\mathrm {NSPACE} } {\log n}$
 * 13.6 Some provably intractable problems
 * 13.7 The $\mathscr P = \mathscr {NP}$ question with Turing machines with oracles:
 * limits on our ability to tell whether $\mathscr P = \mathscr {NP}$


 * Chapter 14 Highlights of Other Important Language Classes
 * 14.1 Auxiliary pushdown automata
 * 14.2 Stack automata
 * 14.3 Indexed languages
 * 14.4 Developmental systems


 * Bibliography


 * Index



Source work progress
* : Chapter $1$: Preliminaries: $1.4$ Set Notation: Infinite sets