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Transition Systems and Regular Events

In: Finite Automata, Their Algebras and Grammars

Author

Listed:
  • J. Richard Büchi

    (Purdue University, Computer Science Department)

  • Dirk Siefkes

    (Technische Universität Berlin, Fachbereich Informatik)

Abstract

We will continue here the study of finite automata behavior, or periodic events, with a presentation of Kleene’s (1956) characterization of these events. In chapter 3 we have already seen a proof of one half of this result, namely, the class P k of periodic events contains all finite subsets of N k , is closed under the Boolean operators, and is closed under the “regular” operators dot and star. Transition systems, also called nondeterministic automata, were introduced by Myhill (1957) to give another, and very elegant, proof of this fact. He noticed that the closure under ∪, · , * is quite obvious for behaviors of finite transition systems, and he used the subset construction to show that these behaviors are no more general than those of finite automata. This matter is contained in sections 4.1, 4.2, and 4.3.

Suggested Citation

  • J. Richard Büchi & Dirk Siefkes, 1989. "Transition Systems and Regular Events," Springer Books, in: Dirk Siefkes (ed.), Finite Automata, Their Algebras and Grammars, chapter 0, pages 133-179, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8853-1_4
    DOI: 10.1007/978-1-4613-8853-1_4
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