Almost-Sure Model-Checking of Reactive Timed Automata

Abstract

Abstract-We consider the model of stochastic timed automata, a model in which both delays and discrete choices are made probabilistically. We are interested in the almost-sure modelchecking problem, which asks whether the automaton satisfies a given property with probability 1. While this problem was shown decidable for single-clock automata few years ago, it was also proven that the algorithm for this decidability result could not be used for general timed automata. In this paper we describe the subclass of reactive timed automata, and we prove decidability of the almost-sure model-checking problem under that restriction. Decidability relies on the fact that this model is almost-surely fair. As a desirable property of real systems, we show that reactive automata are almost-surely non-Zeno. Finally we show that the almost-sure model-checking problem can be decided for specifications given as deterministic timed automata.

A Maximal Entropy Stochastic Process for a Timed Automaton,

“…There are two kind of probabilistic model checking: (i) the almost sure model checking aiming to decide if a model satisfies a formula with probability one (e.g. [16,3]); (ii) the quantitative (probabilistic) model checking (e.g. [14,18]) aiming to compare the probability of a formula to be satisfied with some given threshold or to estimate directly this probability.…”

“…The GSMPs have several differences with TA; roughly they behave as follows: in each location, clocks decrease until a clock is null, at this moment an action corresponding to this clock is fired, the other clocks are either reset, unchanged or purely canceled. Our probability setting is more inspired by [9,16,18] where probability densities are added directly on the TA. Here we add the new feature of an initial probability density function on states.…”

Transient Analysis of Networks of Stochastic Timed Automata Using Stochastic State Classes

“…This has consequences on the PDFs that are possible in a location, but also on the structure of the underlying timed automaton itself. However, natural large classes of stochastic timed automata such as reactive STA [10] are covered in our framework.…”

“…For single-clock STA, almost-sure verification of LTL specifications was shown decidable [6] and an approximated technique for quantitative model-checking was proposed [8]. Decidability of almost sure verification was also shown for reactive timed automata [10], even with multiple-clocks but under restrictions on sojourn times.…”

Playing Optimally on Timed Automata with Random Delays

“…For technical convenience-and following [6]-we require our (probabilistic) timed automata to be reactive. A (probabilistic) timed automaton A = (L, X, E) is called reactive if, for each state s = ( , v) of A, there is an edge e ∈ E such that s 0,e − − → s for some state s of A.…”