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On the Effects of Nondeterminism on Ordered Restarting Automata

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SOFSEM 2016: Theory and Practice of Computer Science (SOFSEM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9587))

Abstract

While (stateless) deterministic ordered restarting automata accept exactly the regular languages, it is known that nondeterministic ordered restarting automata accept some languages that are not context-free. Here we show that, in fact, the class of languages accepted by these automata is an abstract family of languages that is incomparable to the linear languages, the context-free languages, and the growing context-sensitive languages with respect to inclusion, and that the emptiness problem is decidable for these languages. In addition, it is shown that stateless ordered restarting automata just accept regular languages, and we present an infinite family of regular languages \(C_n\) such that \(C_n\) is accepted by a stateless ordered restarting automaton with an alphabet of size O(n), but each stateless deterministic ordered restarting automaton for \(C_n\) needs \(2^{O(n)}\) letters.

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Notes

  1. 1.

    Following the notation that is used for restarting automata in general (see, e.g., [10]), the suffix -WW says that this automaton can rewrite using non-input symbols.

  2. 2.

    A meta-instruction \((E,u\rightarrow v)\) is applicable to a restarting configuration \(q_0\rhd w\lhd \), if w can be factored as \(w=w_1uw_2\) such that \(\rhd w_1\in E\), which would give the cycle \(q_0\rhd w\lhd \vdash _M^c q_0\rhd w_1vw_2\lhd \), and a meta-instruction \((E,{\textsf {Accept}})\) allows M to accept from any restarting configuration \(q_0\rhd w\lhd \) such that \(\rhd w\lhd \in E\) (see, e.g., [10]).

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Authors and Affiliations

  1. Fachbereich Elektrotechnik/Informatik, Universität Kassel, 34109, Kassel, Germany

    Kent Kwee & Friedrich Otto

Authors
  1. Kent Kwee
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  2. Friedrich Otto
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Correspondence to Friedrich Otto .

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Editors and Affiliations

  1. University of Latvia, Riga, Latvia

    Rūsiņš Mārtiņš Freivalds

  2. University of Paderborn, Paderborn, Germany

    Gregor Engels

  3. University of Genoa, Genoa, Italy

    Barbara Catania

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Kwee, K., Otto, F. (2016). On the Effects of Nondeterminism on Ordered Restarting Automata. In: Freivalds, R., Engels, G., Catania, B. (eds) SOFSEM 2016: Theory and Practice of Computer Science. SOFSEM 2016. Lecture Notes in Computer Science(), vol 9587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49192-8_30

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  • DOI: https://doi.org/10.1007/978-3-662-49192-8_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-49191-1

  • Online ISBN: 978-3-662-49192-8

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