Author	Kozen, Dexter C. author
Title	Automata and Computability [electronic resource] / by Dexter C. Kozen
Imprint	New York, NY : Springer New York : Imprint: Springer, 1997
Connect to	http://dx.doi.org/10.1007/978-1-4612-1844-9
Descript	XIII, 400 p. online resource

The aim of this textbook is to provide undergraduate students with an introduction to the basic theoretical models of computability, and to develop some of the model's rich and varied structure. Students who have already some experience with elementary discrete mathematics will find this a well-paced first course, and a number of supplementary chapters introduce more advanced concepts. The first part of the book is devoted to finite automata and their properties. Pushdown automata provide a broader class of models and enable the analysis of context-free languages. In the remaining chapters, Turing machines are introduced and the book culminates in discussions of effective computability, decidability, and Gรถdel's incompleteness theorems. Plenty of exercises are provided, ranging from the easy to the challenging. As a result, this text will make an ideal first course for students of computer science

Lectures -- 1 Course Roadmap and Historical Perspective -- 2 Strings and Sets -- 3 Finite Automata and Regular Sets -- 4 More on Regular Sets -- 5 Nondeterministic Finite Automata -- 6 The Subset Construction -- 7 Pattern Matching -- 8 Pattern Matching and Regular Expressions -- 9 Regular Expressions and Finite Automata -- A Kleene Algebra and Regular Expressions -- 10 Homomorphisms -- 11 Limitations of Finite Automata -- 12 Using the Pumping Lemma -- 13 DFA State Minimization -- 14 A Minimization Algorithm -- 15 MyhillโNerode Relations -- 16 The MyhillโNerode Theorem -- B Collapsing Nondeterministic Automata -- C Automata on Terms -- D The MyhillโNerode Theorem for Term Automata -- 17 Two-Way Finite Automata -- 18 2DFAs and Regular Sets -- 19 Context-Free Grammars and Languages -- 20 Balanced Parentheses -- 21 Normal Forms -- 22 The Pumping Lemma for CFLs -- 23 Pushdown Automata -- E Final State Versus Empty Stack -- 24 PDAs and CFGs -- 25 Simulating NPDAs by CFGs -- F Deterministic Pushdown Automata -- 26 Parsing -- 27 The CockeโKasamiโYounger Algorithm -- G The ChomskyโSchรผtzenberger Theorem -- H Parikhโs Theorem -- 28 Turing Machines and Effective Computability -- 29 More on Turing Machines -- 30 Equivalent Models -- 31 Universal Machines and Diagonalization -- 32 Decidable and Undecidable Problems -- 33 Reduction -- 34 Riceโs Theorem -- 35 Undecidable Problems About CFLs -- 36 Other Formalisms -- 37 The a-Calculus -- I While Programs -- J Beyond Undecidability -- 38 Gรถdelโs Incompleteness Theorem -- 39 Proof of the Incompleteness Theorem -- K Gรถdelโs Proof -- Exercises -- Homework Sets -- Homework 1 -- Homework 2 -- Homework 3 -- Homework 4 -- Homework 5 -- Homework 6 -- Homework 7 -- Homework 8 -- Homework 9 -- Homework 10 -- Homework 11 -- Homework 12 -- Miscellaneous Exercises -- Finite Automata and Regular Sets -- Pushdown Automata and Context-Free Languages -- Turing Machines and Effective Computability -- Hints and Solutions -- Hints for Selected Miscellaneous Exercises -- Solutions to Selected Miscellaneous Exercises -- References -- Notation and Abbreviations

1. Computer science
2. Computers
3. Algorithms
4. Computer Science
5. Computation by Abstract Devices
6. Algorithm Analysis and Problem Complexity