Quantitative extensions of temporal logics have recently#N#attracted significant attention. In this work, we study#N#frequency LTL (fLTL), an extension of LTL which allows to speak#N#about frequencies of events along an execution. Such an#N#extension is particularly useful for probabilistic systems that#N#often cannot fulfil strict qualitative guarantees on the#N#behaviour. It has been recently shown that controller synthesis#N#for Markov decision processes and fLTL is decidable when all#N#the bounds on frequencies are 1. As a step towards a complete#N#quantitative solution, we show that the problem is decidable#N#for the fragment fLTL\GU, where U does not occur in the scope#N#of G (but still F can). Our solution is based on a novel#N#translation of such quantitative formulae into equivalent#N#deterministic automata.
['Vojtěch Forejt', 'Jan Krčál', 'Jan Křetínský']
Controller Synthesis for MDPs and Frequency LTL\GU