Given a model and a specification, the fundamental model-checking problem asks for algorithmic verification of whether the model satisfies the specification. We consider graphs and Markov decision processes (MDPs), which are fundamental models for reactive systems. One of the very basic specifications that arise in verification of reactive systems is the strong fairness (aka Streett) objective. Given different types of requests and corresponding grants, the objective requires that for each type, if the request event happens infinitely often, then the corresponding grant event must also happen infinitely often. All ω -regular objectives can be expressed as Streett objectives and hence they are canonical in verification. To handle the state-space explosion, symbolic algorithms are required that operate on a succinct implicit representation of the system rather than explicitly accessing the system. While explicit algorithms for graphs and MDPs with Streett objectives have been widely studied, there has been no improvement of the basic symbolic algorithms. The worst-case numbers of symbolic steps required for the basic symbolic algorithms are as follows: quadratic for graphs and cubic for MDPs. In this work we present the first sub-quadratic symbolic algorithm for graphs with Streett objectives, and our algorithm is sub-quadratic even for MDPs. Based on our algorithmic insights we present an implementation of the new symbolic approach and show that it improves the existing approach on several academic benchmark examples.
Acknowledgements. K. C. and M. H. are partially supported by the Vienna Science and Technology Fund (WWTF) grant ICT15-003. K. C. is partially supported by the Austrian Science Fund (FWF): S11407-N23 (RiSE/SHiNE), and an ERC Start Grant (279307: Graph Games). V. T. is partially supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie Grant Agreement No. 665385.
CAV: Computer Aided Verification
Oxford, United Kingdom
2018-07-14 – 2018-07-17
Chatterjee K, Henzinger MH, Loitzenbauer V, Oraee S, Toman V. Symbolic algorithms for graphs and Markov decision processes with fairness objectives. In: Vol 10982. Springer; 2018:178-197. doi:10.1007/978-3-319-96142-2_13
Chatterjee, K., Henzinger, M. H., Loitzenbauer, V., Oraee, S., & Toman, V. (2018). Symbolic algorithms for graphs and Markov decision processes with fairness objectives (Vol. 10982, pp. 178–197). Presented at the CAV: Computer Aided Verification, Oxford, United Kingdom: Springer. https://doi.org/10.1007/978-3-319-96142-2_13
Chatterjee, Krishnendu, Monika H Henzinger, Veronika Loitzenbauer, Simin Oraee, and Viktor Toman. “Symbolic Algorithms for Graphs and Markov Decision Processes with Fairness Objectives,” 10982:178–97. Springer, 2018. https://doi.org/10.1007/978-3-319-96142-2_13.
K. Chatterjee, M. H. Henzinger, V. Loitzenbauer, S. Oraee, and V. Toman, “Symbolic algorithms for graphs and Markov decision processes with fairness objectives,” presented at the CAV: Computer Aided Verification, Oxford, United Kingdom, 2018, vol. 10982, pp. 178–197.
Chatterjee K, Henzinger MH, Loitzenbauer V, Oraee S, Toman V. 2018. Symbolic algorithms for graphs and Markov decision processes with fairness objectives. CAV: Computer Aided Verification, LNCS, vol. 10982, 178–197.
Chatterjee, Krishnendu, et al. Symbolic Algorithms for Graphs and Markov Decision Processes with Fairness Objectives. Vol. 10982, Springer, 2018, pp. 178–97, doi:10.1007/978-3-319-96142-2_13.
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