Probabilistic Bisimulation and Simulation Algorithms by Abstract Interpretation

Abstract

Abstract. We show how bisimulation equivalence and simulation preorder on probabilistic LTSs (PLTSs), namely the main behavioural relations on probabilistic nondeterministic processes, can be characterized by abstract interpretation. Both bisimulation and simulation can be obtained as completions of partitions and preorders, viewed as abstract domains, w.r.t. a pair of concrete functions that encode a PLTS. As a consequence, this approach provides a general framework for designing algorithms for computing bisimulation and simulation on PLTSs. Notably, (i) we show that the standard bisimulation algorithm by Baier et al. can be viewed as an instance of such a framework and (ii) we design a new efficient simulation algorithm that improves the state of the art.

Bisimulation and simulation algorithms on probabilistic transition systems by abstract interpretation

“…On the other hand, we show that the corresponding complete shell for computing the simulation preorder yields a new efficient probabilistic simulation algorithm that advances the state of the art: in fact, its time and space complexity bounds improve on the best known simulation algorithm for PLTSs by Zhang et al [20]. This is an extended and revised version of the conference paper [4].…”

Computing Behavioral Relations for Probabilistic Concurrent Systems

“…To a careful observer, flow and optimization problems and probabilistic concurrent systems are not so unrelated, since the probability mass concentrated in the initial state can be seen as a liquid that flows and distributes in the network representing the possible evolution of the system. To highlight this connection, in this survey we consider a selection of papers [29,30,55,57] that, together with other works in concurrency literature such as [2,4,13,15,20,21,43,45], make use of flow and optimization problems to decide or solve efficiently the challenges of probabilistic concurrent systems.…”

“…It is worthwhile to note that by combining a preflow approach, as the one adopted for Smf, and abstract interpretation techniques, the complexity can be reduced to O(N 3 ) for simulation and O(N 2 • log N ) for bisimulation [15].…”

Logical Characterizations of Behavioral Relations on Transition Systems of Probability Distributions

“…As a further avenue of future work we plan to study whether and how behavioral relations on PLTSs can be computed by resorting to standard algorithms for LTSs that compute the corresponding lifted relations on a dLTS. A first step in this direction has been taken in [Crafa and Ranzato 2011a;Crafa and Ranzato 2012], where efficient algorithms to compute simulation and bisimulation on PLTSs have been derived by resorting to abstract interpretation techniques.…”