Universality of Regular Realizability Problems

  • Mikhail N. Vyalyi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7913)


A regular realizability (RR) problem is to test nonemptiness of the intersection of some fixed language (filter) with a given regular language. We show that RR problems are universal in the following sense. For any language L there exists an RR problem equivalent to L under disjunctive reductions on nondeterministic log space.

We deduce from this result the existence of RR problems complete under polynomial reductions for many complexity classes including all classes of the polynomial hierarchy.


Complexity Class Regular Language Binary Word Polynomial Hierarchy Mathematical System Theory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mikhail N. Vyalyi
    • 1
  1. 1.Dorodnitsyn Computing CenterRussian Academy of ScienceRussia

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