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Controller Synthesis for MDPs and Frequency LTL\GU

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FOREJT Vojtěch KRČÁL Jan KŘETÍNSKÝ Jan

Druh Článek ve sborníku
Konference LPAR 2015
Citace
Doi http://dx.doi.org/10.1007/978-3-662-48899-7_12
Obor Informatika
Klíčová slova frequency LTL; quantitative logics; MDP controller synthesis; automata characterization
Popis Quantitative extensions of temporal logics have recently attracted significant attention. In this work, we study frequency LTL (fLTL), an extension of LTL which allows to speak about frequencies of events along an execution. Such an extension is particularly useful for probabilistic systems that often cannot fulfil strict qualitative guarantees on the behaviour. It has been recently shown that controller synthesis for Markov decision processes and fLTL is decidable when all the bounds on frequencies are 1. As a step towards a complete quantitative solution, we show that the problem is decidable for the fragment fLTL\GU, where U does not occur in the scope of G (but still F can). Our solution is based on a novel translation of such quantitative formulae into equivalent deterministic automata.
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