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Mean-Payoff Games on Timed Automata

Authors Shibashis Guha, Marcin Jurdzinski, Shankara Narayanan Krishna, Ashutosh Trivedi

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Shibashis Guha
Marcin Jurdzinski
Shankara Narayanan Krishna
Ashutosh Trivedi

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Shibashis Guha, Marcin Jurdzinski, Shankara Narayanan Krishna, and Ashutosh Trivedi. Mean-Payoff Games on Timed Automata. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.FSTTCS.2016.44

Abstract

Mean-payoff games on timed automata are played on the infinite weighted graph of configurations of priced timed automata between two players - Player Min and Player Max - by moving a token along the states of the graph to form an infinite run. The goal of Player Min is to minimize the limit average weight of the run, while the goal of the Player Max is the opposite. Brenguier, Cassez, and Raskin recently studied a variation of these games and showed that mean-payoff games are undecidable for timed automata with five or more clocks. We refine this result by proving the undecidability of mean-payoff games with three clocks. On a positive side, we show the decidability of mean-payoff games on one-clock timed automata with binary price-rates. A key contribution of this paper is the application of dynamic programming based proof techniques applied in the context of average reward optimization on an uncountable state and action space.

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Keywords
  • Timed Automata
  • Mean-Payoff Games
  • Controller-Synthesis

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