Roadmap of Infinite Results

Abstract

Abstract. This paper provides a comprehensive summary of equivalence checking results for infinite-state systems. References to the relevant papers will be updated continuously according to the development in the area. The most recent version of this document is available from the web-page

Undecidability Results for Bisimilarity on Prefix Rewrite Systems

“…This has initiated several research directions, one of them exploring the decidability and complexity questions for bisimilarity. The obtained results differ from those known in the case of classical language equivalence; we can refer to surveys like [3,25].…”

Bisimilarity in Fresh-Register Automata

“…Consequently, the algorithmics of bisimilarity have attracted a lot of attention from researchers interested in the theory and practice of equivalence checking. When the set of observable actions available to a system is finite, a lot is already known about the complexity of the problem for specific classes of systems, although tight bounds are often difficult to obtain in the infinite-state cases [26]. In this paper we prove a number of bounds on the complexity of bisimulation equivalence checking.…”

“…The complexity of bisimilarity problems has been studied extensively in the finite-alphabet setting and the current state of the art for infinite-state systems is summarised nicely in [26]. Recent papers concerning the complexity of decision problems for register automata have, until now, not considered bisimulation equivalence.…”

Bisimilarity of One-Counter Processes Is PSPACE-Complete

“…In the last twenty years a lot of research has been devoted to checking behavioral equivalence of infinite-state systems, see [23] for an up-to-date record. In the setting of infinite-state systems, see also [14] for Mayr's classification of infinite-state systems, the situation is less clear.…”