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On the Complexity of 2-Monotone Restarting Automata

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Abstract

The \(\mathsf{R}\) -automaton is the weakest form of the nondeterministic version of the restarting automaton that was introduced by Jančar et al. to model the so-called analysis by reduction. Here it is shown that the class ℒ(R) of languages that are accepted by \(\mathsf{R}\) -automata is incomparable under set inclusion to the class \(\mathsf{CRL}\) of Church-Rosser languages and to the class \(\mathsf{GCSL}\) of growing context-sensitive languages. In fact this already holds for the class \(\mathcal{L}(\mbox{2-\textsf {mon-R}})\) of languages that are accepted by 2-monotone \(\mathsf{R}\) -automata. In addition, we prove that already the latter class contains \(\mathsf{NP}\) -complete languages, showing that already the 2-monotone \(\mathsf{R}\) -automaton has a surprisingly large expressive power.

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Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, 51-151, Wrocław, Poland

    Tomasz Jurdziński

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

    Friedrich Otto

  3. Department of Computer Science, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    František Mráz & Martin Plátek

Authors
  1. Tomasz Jurdziński
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  2. Friedrich Otto
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  3. František Mráz
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  4. Martin Plátek
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Corresponding author

Correspondence to Friedrich Otto.

Additional information

The results of this paper have been announced at DLT 2004 in Auckland, New Zealand.

This work was mainly carried out while T. Jurdziński was visiting the University of Kassel, supported by a grant from the Deutsche Forschungsgemeinschaft (DFG).

F. Mráz and M. Plátek were partially supported by the Grant Agency of the Czech Republic under Grant-No. 201/04/2102 and by the program ‘Information Society’ under project 1ET100300517. F. Mráz was also supported by the Grant Agency of Charles University in Prague under Grant-No. 358/2006/A-INF/MFF.

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Jurdziński, T., Otto, F., Mráz, F. et al. On the Complexity of 2-Monotone Restarting Automata. Theory Comput Syst 42, 488–518 (2008). https://doi.org/10.1007/s00224-007-9004-y

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