CEGAR for Qualitative Analysis of Probabilistic Systems

• Published in: Computer Aided Verification pp. 473 - 490
• Main Authors: Chatterjee, Krishnendu, Chmelík, Martin, Daca, Przemysław
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Atomic Proposition; Markov Decision Process; Simulation Relation; Stochastic Game; Winning Strategy
• ISBN: 3319088661; 9783319088662
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-08867-9_31

We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems.We focus on qualitative properties forMDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability. We introduce a new simulation relation to capture the refinement relation ofMDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.We present an automated technique for assume-guarantee style reasoning for compositional analysis ofMDPs with qualitative properties by giving a counterexample guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.