Undecidability of Cost-Bounded Reachability in Priced Probabilistic Timed Automata

Authors:
Jasper Berendsen;Taolue Chen;David N. Jansen
Affiliations:
Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands;Department of Software Engineering, CWI, Amsterdam, The Netherlands;Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands
Venue:
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Year:
2009

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Abstract

Priced Probabilistic Timed Automata (PPTA) extend timed automata with cost-rates in locations and discrete probabilistic branching. The model is a natural combination of Priced Timed Automata and Probabilistic Timed Automata. In this paper we focus on cost-bounded probabilistic reachability for PPTA, which determines if the maximal probability to reach a goal location within a given cost bound (and time bound) exceeds a threshold p *** (0,1]. We prove undecidability of the problem for simple PPTA in 3 variants: with 3 clocks and stopwatch cost-rates or strictly positive cost-rates. Because we encode a 2-counter machine in a new way, we can also show undecidability for cost-rates in *** and only 2 clocks.