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Reversible Limited Automata

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Book cover Machines, Computations, and Universality (MCU 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9288))

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Abstract

A k-limited automaton is a linear bounded automaton that may rewrite each tape square only in the first k visits, where \(k\ge 0\) is a fixed constant. It is known that these automata accept context-free languages only. We investigate deterministic k-limited automata towards their ability to perform reversible computations, that is, computations in which every configuration has at most one predecessor. A first result is that, for all \(k\ge 0\), sweeping k-limited automata accept regular languages only. In contrast to reversible finite automata, all regular languages are accepted by sweeping 0-limited automata. Then we study the computational power gained in the number k of possible rewrite operations. It is shown that the reversible 2-limited automata accept regular languages only and, thus, are strictly weaker than general 2-limited automata. Furthermore, a proper inclusion between reversible 3-limited and 4-limited automata languages is obtained. The next levels of the hierarchy are separated between every k and \(k+3\) rewrite operations. Finally, it turns out that all k-limited automata accept Church-Rosser languages only, that is, the intersection between context-free and Church-Rosser languages contains an infinite hierarchy of language families beyond the deterministic context-free languages.

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Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Martin Kutrib & Matthias Wendlandt

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  1. Martin Kutrib
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  2. Matthias Wendlandt
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Correspondence to Martin Kutrib .

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Editors and Affiliations

  1. Université d'Orléans, Orléans, France

    Jerome Durand-Lose

  2. Eastern Mediterranean University, Famagusta, Cyprus

    Benedek Nagy

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Kutrib, M., Wendlandt, M. (2015). Reversible Limited Automata. In: Durand-Lose, J., Nagy, B. (eds) Machines, Computations, and Universality. MCU 2015. Lecture Notes in Computer Science(), vol 9288. Springer, Cham. https://doi.org/10.1007/978-3-319-23111-2_8

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  • DOI: https://doi.org/10.1007/978-3-319-23111-2_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23110-5

  • Online ISBN: 978-3-319-23111-2

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