Probabilistic Timed Automata with One Clock and Initialised Clock-Dependent Probabilities

TL;DR

This paper introduces a polynomial-time method for solving reachability problems in a specific subclass of one-clock clock-dependent probabilistic timed automata, using a transformation to interval Markov decision processes.

Contribution

It defines a new subclass of automata with affine clock dependencies and initialisation conditions, and provides a polynomial-time solution approach for their reachability problems.

Findings

Polynomial-time solution for reachability problems

Transformation to interval Markov decision processes

Applicable to automata with affine clock dependencies

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.