Model Checking the Quantitative μ-Calculus on Linear Hybrid Systems
In this work, we consider the model-checking problem for a quantitative extension of the modal μ-calculus on a class of hybrid systems. Qualitative model checking has been proved decidable and implemented for several classes of systems, but this is not the case for quantitative questions, which arise naturally in this context. Recently, quantitative formalisms that subsume classical temporal logics and additionally allow to measure interesting quantitative phenomena were introduced. We show how a powerful quantitative logic, the quantitative μ-calculus, can be model-checked with arbitrary precision on initialised linear hybrid systems. To this end, we develop new techniques for the discretisation of continuous state spaces based on a special class of strategies in model-checking games and show decidability of a class of counter-reset games that may be of independent interest.
KeywordsModel Check Hybrid System Discrete Strategy Hybrid Automaton Arbitrary Precision
Unable to display preview. Download preview PDF.
- 2.Colcombet, T., Löding, C.: Regular cost functions over finite trees. In: LICS, pp. 70–79. IEEE Computer Society, Los Alamitos (2010)Google Scholar
- 5.Figueira, D., Figueira, S., Schmitz, S., Schnoebelen, P.: Ackermann and primitive-recursive bounds with dickson’s lemma. CoRR, abs/1007.2989 (2010)Google Scholar
- 9.Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? In: Proceedings of STOC 1995, pp. 373–382. ACM, New York (1995)Google Scholar
- 11.McIver, A., Morgan, C.: Results on the quantitative μ-calculus qMμ. ACM Trans. Comput. Log. 8(1) (2007)Google Scholar