On the complexity of equation solving in process algebra

• The problem of designing a system which in a given environment C should satisfy a given specification S can be formulated as "find a system P such that C(P) satisfies the specification S". In process algebra, such problems take the form of equations. We investigate the complexity of solving such equations in process algebra. We consider the problem of deciding whether there is a process P which satisfies an equation of one of the following forms : (the complete form could not be translated) where C is an arbitrary context of some process Algebra, A, B and Q are given processes, S is a modal specification, (˜) is (weak) bisimulation equivalence, is refinement between modal specifications (a generalization of bisimulation equivalence), and | and \L is the parallel and restriction operator of CCS respectively. The main result is that all four problems are PSPACE-hard in the size of the given contexts, processes and specifications. The four problems are still PSPACE-hard if the right-hand side of the equations is required to be deterministic and the number of involved actions is bounded by a small constant. We also give constraints under which the first and third problem can be solved in polynomial time.

Subject headings

NATURVETENSKAP  -- Data- och informationsvetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences (hsv//eng)

Publication and Content Type

vet (subject category)

rap (subject category)