Abstract
Clock-dependent probabilistic timed automata extend classical timed automata with discrete probabilistic choice, where the probabilities are allowed to depend on the exact values of the clocks. Previous work has shown that the quantitative reachability problem for clock-dependent probabilistic timed automata with at least three clocks is undecidable. In this paper, we consider the subclass of clock-dependent probabilistic timed automata that have one clock, that have clock dependencies described by affine functions, and that satisfy an initialisation condition requiring that, at some point between taking edges with non-trivial clock dependencies, the clock must have an integer value. We present an approach for solving in polynomial time quantitative and qualitative reachability problems of such one-clock initialised clock-dependent probabilistic timed automata. Our results are obtained by a transformation to interval Markov decision processes.
Highlights
The diffusion of complex systems with timing requirements that operate in unpredictable environments has led to interest in formal modelling and verification techniques for timed and probabilistic systems
Timed automata and Markov decision processes have been combined to obtain the formalism of probabilistic timed automata [GJ95, KNSS02, NPS13], which can be viewed as timed automata with probabilities associated with their edges
We have presented a method for the transformation of a class of 1c-cdPTAs to interval Markov decision process (IMDP) such that there is a precise relationship between the schedulers of the 1c-cdPTA and the IMDP, allowing us to use established polynomial-time algorithms for IMDPs to decide quantitative and qualitative reachability problems on the 1c-cdPTA
Summary
The diffusion of complex systems with timing requirements that operate in unpredictable environments has led to interest in formal modelling and verification techniques for timed and probabilistic systems. A well-established modelling formalism for timed systems is timed automata [AD94]. To model probabilistic systems formally, frameworks such as Markov chains or Markov decision processes are used typically. Model-checking algorithms for these formalisms have been presented in the literature: for overviews of these techniques see, for example, [BFL+18] for timed automata, and [BK08, FKNP11] for Markov chains and Markov decision processes. Timed automata and Markov decision processes have been combined to obtain the formalism of probabilistic timed automata [GJ95, KNSS02, NPS13], which can be viewed as timed automata with probabilities associated with their edges (or, equivalently, as Markov decision processes equipped with clocks and their associated constraints)
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