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Equations Over Languages and Finite Automata

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Abstract

An alphabet is a finite set of symbols. The set of all finite strings over a fixed alphabet X is denoted by X . X includes the empty string ε. A subset LX is called a language over alphabet X.

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Notes

  1. 1.

    By the given definition in agreement with standard textbooks (see  [63]), a DFA must be a complete FA, but a complete FA does not need to be deterministic.

  2. 2.

    This definition is an abstraction to languages of the most common definition of Moore automata/finite state machines.

  3. 3.

    Use the same order I ×U ×O in the languages (L 1) ↑O and (L 2) ↑I .

  4. 4.

    It is not uncommon in practice to find that \(\vert \tilde{S}\vert \leq \vert S\vert \).

  5. 5.

    Apply the closure construction to obtain an equivalent deterministic finite automaton without ε-moves.

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Correspondence to Tiziano Villa .

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© 2012 Springer Science+Business Media, LLC

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Villa, T., Yevtushenko, N., Brayton, R.K., Mishchenko, A., Petrenko, A., Sangiovanni-Vincentelli, A. (2012). Equations Over Languages and Finite Automata. In: The Unknown Component Problem. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-68759-9_2

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  • DOI: https://doi.org/10.1007/978-0-387-68759-9_2

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  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-34532-1

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