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**Automata theory with modern applications. With contributions by Tom Head.**
*(English)*
Zbl 1127.68049

Cambridge: Cambridge University Press (ISBN 0-521-61324-8/pbk; 0-521-84887-3/hbk; 978-0-511-60720-2/ebook). viii, 255 p. (2006).

This textbook presents in the first five chapters more or less the “standard” programme for any formal language theory course and includes topics such as finite automata, syntactic monoids, minimal automata, pumping lemmata, pushdown automata, grammars, Chomsky and Greibach normal form, equivalence of grammars and automata, Turing machines, halting problem, and undecidable properties of context-free languages. Also the presentation is as usual, with some idiosyncrasy (e.g., the definition of minimal automata, here called intrinsic automata, the definition of nondeterministic Turing machines, a paragraph relating CFGs to nondeterministic Turing machines, and some more).

What makes this textbook unique is its final two chapters, written by Tom Head. Chapter 6, “A visual approach to formal language theory”, is devoted to the area called combinatorics on words and presents material usually not found in an introductory text. Finally, the words “modern applications” in the title of the book are a tribute to the last chapter, in which on 10 pages a glimpse of applications of formal language theory in molecular biology, centered around the notion of a splicing language, is presented.

Every section of the book ends with a number of exercises. The book ends with a bibliography section (with pointers to further literature mainly for the last two chapters) as well a “further reading” section containing links to further textbooks and tutorial papers.

What makes this textbook unique is its final two chapters, written by Tom Head. Chapter 6, “A visual approach to formal language theory”, is devoted to the area called combinatorics on words and presents material usually not found in an introductory text. Finally, the words “modern applications” in the title of the book are a tribute to the last chapter, in which on 10 pages a glimpse of applications of formal language theory in molecular biology, centered around the notion of a splicing language, is presented.

Every section of the book ends with a number of exercises. The book ends with a bibliography section (with pointers to further literature mainly for the last two chapters) as well a “further reading” section containing links to further textbooks and tutorial papers.

Reviewer: Heribert Vollmer (Hannover)

### MSC:

68Q45 | Formal languages and automata |

68-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science |

68Q05 | Models of computation (Turing machines, etc.) (MSC2010) |

68Q10 | Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) |

68Q42 | Grammars and rewriting systems |

68Q70 | Algebraic theory of languages and automata |

68R15 | Combinatorics on words |