Simulation and Bisimulation for Probabilistic Timed Automata

Abstract

Abstract. Probabilistic timed automata are an extension of timed automata with discrete probability distributions. Simulation and bisimulation relations are widely-studied in the context of the analysis of system models, with applications in the stepwise development of systems and in model reduction. In this paper, we study probabilistic timed simulation and bisimulation relations for probabilistic timed automata. We present an EXPTIME algorithm for deciding whether two probabilistic timed automata are probabilistically timed similar or bisimilar. Furthermore, we consider a logical characterization of probabilistic timed bisimulation.

Encoding Timed Models as Uniform Labeled Transition Systems

“…A probabilistic extension of the TLTS model (PTLTS) was introduced in [19]. Following the simple probabilistic automaton model of [18], the action-transition relation is transformed into a probabilistic action-transition relation.…”

“…While in [19] there is a single transition relation and hence each transition is also labeled with the duration of the corresponding action, here we stick to the orthogonal-time approach and hence keep using two transition relations: a probabilistic one labeled with actions and a deterministic one labeled with amounts of time. We prefer to do so for two reasons.…”

“…A notion of bisimilarity for probabilistic timed processes was introduced in [19], where a modal logic characterization and a decision procedure were also studied. Below, we reformulate the definition in the orthogonal-time framework and we let D(C) = s∈C D(s) for D ∈ Distr cs (S) and C ⊆ S. Definition 12.…”

“…In Sect. 5, we encode as ULTraS the variant of LTS underlying PTA and we show that two different bisimilarities can be defined: the one in [19] and a new one for which we exhibit a modal logic characterization. In Sects.…”

Time-Abstracting Bisimulation for Markovian Timed Automata

“…In general, the problem of computing bisimular states of infinite transition systems is not decidable and to cope with this problem, many modified versions of bisimulation relations have been proposed. For example, in [2] timed bisimulation and probabilistic timed bisimulation have been studied. In [3] the concept of week bisimulation for PTA has been introduced and a definition for sets of states, called classes, has been utilized in order to overcome the problem of infinite states.…”