Stochastic Timed Automata

TL;DR

This paper investigates the almost-sure model-checking problem for stochastic timed automata, proposing a finite abstraction called the thick graph to decide properties with probability 1, applicable to certain classes of automata.

Contribution

It introduces the thick graph abstraction for stochastic timed automata and establishes conditions under which almost-sure model-checking is decidable, extending verification techniques.

Findings

Decidability of almost-sure model-checking for specific classes of stochastic timed automata.

Construction of the thick graph as a finite Markov chain abstraction.

Automata are almost-surely fair in classes like single-clock and weak-reactive automata.

Abstract

A stochastic timed automaton is a purely stochastic process defined on a timed automaton, in which both delays and discrete choices are made randomly. We study the almost-sure model-checking problem for this model, that is, given a stochastic timed automaton A and a property $\Phi$, we want to decide whether A satisfies $\Phi$ with probability 1. In this paper, we identify several classes of automata and of properties for which this can be decided. The proof relies on the construction of a finite abstraction, called the thick graph, that we interpret as a finite Markov chain, and for which we can decide the almost-sure model-checking problem. Correctness of the abstraction holds when automata are almost-surely fair, which we show, is the case for two large classes of systems, single- clock automata and so-called weak-reactive automata. Techniques employed in this article gather tools from real-time verification and probabilistic verification, as well as topological games played on timed automata.