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[JKNT09] M. Jurdzinski, M. Kwiatkowska, G. Norman and A. Trivedi. Concavely-Priced Probabilistic Timed Automata. In M. Bravetti and G. Zavattaro (editors), Proc. 20th Int. Conf. Concurrency Theory (CONCUR'09), volume 5710 of LNCS, pages 415-430, Springer. September 2009. [pdf] [bib]
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Notes: An full version of this paper with proofs can be found in [JKNT09b] The original publication is available at link.springer.com.
Abstract. Concavely-priced probabilistic timed automata, an extension of probabilistic timed automata, are introduced. In this paper we consider expected reachability, discounted, and average price problems for concavely-priced probabilistic timed automata for arbitrary initial states. We prove that these problems are EXPTIME-complete for probabilistic timed automata with two or more clocks and PTIME-complete for automata with one clock. Previous work on expected price problems for probabilistic timed automata was restricted to expected reachability for linearly-priced automata and integer valued initial states. This work uses the boundary region graph introduced by Jurdzinski and Trivedi to analyse properties of concavely-priced (non-probabilistic) timed automata.