Controller Synthesis for MDPs and Frequency LTL\GU

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Authors

FOREJT Vojtěch KRČÁL Jan KŘETÍNSKÝ Jan

Year of publication 2015
Type Article in Proceedings
Conference LPAR 2015
MU Faculty or unit

Faculty of Informatics

Citation
Doi http://dx.doi.org/10.1007/978-3-662-48899-7_12
Field Informatics
Keywords frequency LTL; quantitative logics; MDP controller synthesis; automata characterization
Description 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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