Verifying abstractions of timed systems

Simulation and Bisimulation for Probabilistic Timed Automata

“…Our approach is to extend the techniques of [12,13], which were applied to non-probabilistic timed automata/timed games, to the case of PTA. We focus our attention on the case of timed simulation.…”

“…We now recall the definition of a finite set Times ((l A , v A ), (l B , v B )) of time durations from [12,13]; it will suffice to consider only the time durations in this set in the subsequent algorithm. ∈ N and 1 ≤ c ≤ c max − min(v A , v B )}.…”

“…Simulation and bisimulation relations have been considered for real-time systems: in this paper we consider timed (rather than time-abstract) versions of these relations. Deciding timed simulation and bisimulation for timed systems is in EXPTIME [11,12]. Similarly, deciding timed alternating (bi)simulation for timed games, which can be used to model real-time controller synthesis problems, is also in EXPTIME [13].…”

“…Such timed simulation and bisimulation relations for Segala's probabilistic automata enriched with timing durations have been presented in [4]. Given that probabilistic timed automata are a generalization of both timed automata and Segala's probabilistic automata, our algorithm is inspired by [12,13] for timing aspects, and by [14,15] for probabilistic aspects. More precisely, a variant of the classical region graph is constructed from two probabilistic timed automata, on which an operator, which can determine whether sets of states are related using certain sub-procedures taken from [14,15], is iterated.…”

“…However, although introducing a region-graph construction, the possibility of obtaining an algorithm was mentioned only briefly. In particular, the key concept of a finite sampling of timing durations [11,12] was missing, and the definition of how to relate probability distributions at the region-graph level was incomplete. Instead we provide a detailed description of an algorithm.…”