Hierarchies in Fragments of Monadic Strict NP

We expose a strict hierarchy within monotone monadic strict NP without 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 strict NP (MSNP). Our hierarchy results apply over a uniform signature involving a single binary relation, that is over digraphs.

• Type: Conference
• Year: 2007
• Where: CIE
• Authors: Barnaby Martin, Florent R. Madelaine
• Keywords: CIE 2007, Monadic Strict Np, Strict Hierarchy, finer Strict Hierarchy