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 ℤ and only 2 clocks.
Research supported by NWO/EW project 612.000.103 FRAAI, the Dutch Bsik project BRICKS. and the European Community’s 7th Framework Programme No. 214755 (QUASIMODO).
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Berendsen, J., Chen, T., Jansen, D.N. (2009). Undecidability of Cost-Bounded Reachability in Priced Probabilistic Timed Automata. In: Chen, J., Cooper, S.B. (eds) Theory and Applications of Models of Computation. TAMC 2009. Lecture Notes in Computer Science, vol 5532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02017-9_16
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DOI: https://doi.org/10.1007/978-3-642-02017-9_16
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