Hierarchies in Fragments of Monadic Strict NP

Authors:
Barnaby Martin;Florent Madelaine
Affiliations:
Department of Computer Science, University of Durham, Science Labs, South Road, Durham DH1 3LE, U.K.;Department of Computer Science, University of Durham, Science Labs, South Road, Durham DH1 3LE, U.K.
Venue:
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Year:
2007

Citing 3
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Abstract

We expose a strict hierarchy within monotone monadic strictNPwithout inequalities(MMSNP), based on the number of second-order monadic quantifiers. We do this by studying a finer strict hierarchy within a class of forbidden patterns problems(FPP), based on the number of permitted colours. Through an adaptation of a preservation theorem of Feder and Vardi, we are able to prove that this strict hierarchy also exists in monadic strictNP (MSNP). Our hierarchy results apply over a uniform signature involving a single binary relation, that is over digraphs.