On expressive power of regular realizability problems

Authors:
M. N. Vyalyi
Affiliations:
Computing Center of the Russian Academy of Sciences, Moscow, Russia
Venue:
Problems of Information Transmission
Year:
2013

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Abstract

A regular realizability (RR) problem is a problem of testing nonemptiness of intersection of some fixed language (filter) with a 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 in nondeterministic log space. From this result, we derive existence of complete problems under polynomial reductions for many complexity classes, including all classes of the polynomial hierarchy.