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From Two-Way to One-Way Finite Automata—Three Regular Expression-Based Methods

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Implementation and Application of Automata (CIAA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9223))

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Abstract

We describe three regular expression-based methods to characterize as a regular language the language defined by a two-way automaton. The construction methods yield relatively simple techniques to directly construct one-way automata that simulate the behavior of two-way automata. The approaches also offer conceptually uncomplicated alternative equivalence proofs of two-way automata and one-way automata, particularly in the deterministic case.

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Notes

  1. 1.

    “It may be tempting to think that it is easy to get a similar condition to acceptance of w by A. It seems that all we have to do is to change the second clause in [the lemma] to \(T_{n+1} \cap F \ne \emptyset \). Unfortunately, this is not the case; to characterize acceptance we also have to demand that the \(T_i\)’s be minimal. While the conditions in the lemma are local, and therefore checkable by a finite-state automaton, minimality is a global condition.” [16], p. 3.

  2. 2.

    Available at https://github.com/mhulden/2nfa.

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Authors and Affiliations

  1. University of Colorado Boulder, Boulder, USA

    Mans Hulden

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  1. Mans Hulden
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Correspondence to Mans Hulden .

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Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

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Hulden, M. (2015). From Two-Way to One-Way Finite Automata—Three Regular Expression-Based Methods. In: Drewes, F. (eds) Implementation and Application of Automata. CIAA 2015. Lecture Notes in Computer Science(), vol 9223. Springer, Cham. https://doi.org/10.1007/978-3-319-22360-5_15

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  • DOI: https://doi.org/10.1007/978-3-319-22360-5_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22359-9

  • Online ISBN: 978-3-319-22360-5

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