Complexity results for POMSET languages

Abstract

Pratt [13] introduced POMSETs (partially ordered multisets) in order to describe and analyze concurrent systems. A POMSET P gives a set of temporal constraints that any correct execution of a given concurrent system must satisfy. Let L(P) (the language of P) denote the set of all system executions that satisfy the constraints given by P. We show the following for finite POMSETs P, Q, and system execution x. • The POMSET Language Membership Problem (given x and P, is ε L(P)?) is NP-complete. • The POMSET Language Containment Problem (given P and Q, is L(P) ⊆ (Q)?) is IIP2 complete. • The POMSET Language Equality Problem (given P and Q, is L(P) = L(Q)?) is at least as hard as the graph-isomorphism problem. • The POMSET Language Size Problem (given P, how many x are in L(P)?) is span-P-complete.