Verifying Probabilistic Timed Automata Against Omega-Regular Dense-Time Properties

TL;DR

This paper addresses the challenge of model-checking probabilistic timed automata against dense-time properties, establishing complexity results and extending the state of the art with nondeterminism and dense-time features.

Contribution

It introduces a product construction for model-checking PTAs against deterministic TAs and proves complexity bounds, extending previous work to nondeterministic TAs and dense-time properties.

Findings

Model-checking PTAs with deterministic TAs is EXPTIME-complete.

Model-checking PTAs with nondeterministic TAs is undecidable.

The work extends the theoretical understanding of dense-time probabilistic automata.

Abstract

Probabilistic timed automata (PTAs) are timed automata (TAs) extended with discrete probability distributions.They serve as a mathematical model for a wide range of applications that involve both stochastic and timed behaviours. In this work, we consider the problem of model-checking linear \emph{dense-time} properties over {PTAs}. In particular, we study linear dense-time properties that can be encoded by TAs with infinite acceptance criterion.First, we show that the problem of model-checking PTAs against deterministic-TA specifications can be solved through a product construction. Based on the product construction, we prove that the computational complexity of the problem with deterministic-TA specifications is EXPTIME-complete. Then we show that when relaxed to general (nondeterministic) TAs, the model-checking problem becomes undecidable.Our results substantially extend state of the art with both the dense-time feature and the nondeterminism in TAs.