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On regular realizability problems

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Abstract

We consider the class of regular realizability problems. Any of such problems is specified by some language (filter) and consists in verifying that the intersection of a given regular language and the filter is nonempty. The main question is diversity of the computational complexity of such problems. We show that any regular realizability problem with an infinite filter is hard for a class of problems decidable in logarithmic space with respect to logarithmic reductions. We give examples of NP-complete and PSPACE-complete regular realizability problems.

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Authors and Affiliations

  1. Computing Center of the Russian Academy of Sciences, Moscow, Russia

    M. N. Vyalyi

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  1. M. N. Vyalyi
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Correspondence to M. N. Vyalyi.

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Original Russian Text © M.N. Vyalyi, 2011, published in Problemy Peredachi Informatsii, 2011, Vol. 47, No. 4, pp. 43–54.

Supported in part by the Russian Foundation for Basic Research, project no. 11-01-00398.

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Vyalyi, M.N. On regular realizability problems. Probl Inf Transm 47, 342–352 (2011). https://doi.org/10.1134/S003294601104003X

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