Learning-Based Compositional Verification for Synchronous Probabilistic Systems

We present novel techniques for automated compositional verification of synchronous probabilistic systems. First, we give an assume-guarantee framework for verifying probabilistic safety properties of systems modelled as discrete-time Markov chains. Assumptions about system components are represented as probabilistic finite automata (PFAs) and the relationship between components and assumptions is captured by weak language inclusion. In order to implement this framework, we develop a semi-algorithm to check language inclusion for PFAs and a new active learning method for PFAs. The latter is then used to automatically generate assumptions for compositional verification.

[1]  Christel Baier,et al.  Principles of Model Checking (Representation and Mind Series) , 2008 .

[2]  Hongyang Qu,et al.  Quantitative Multi-objective Verification for Probabilistic Systems , 2011, TACAS.

[3]  Thomas A. Henzinger,et al.  Compositional Methods for Probabilistic Systems , 2001, CONCUR.

[4]  Lu Feng,et al.  Compositional Verification of Probabilistic Systems Using Learning , 2010, 2010 Seventh International Conference on the Quantitative Evaluation of Systems.

[5]  Rajeev Alur,et al.  A Temporal Logic of Nested Calls and Returns , 2004, TACAS.

[6]  Shobha Vasudevan,et al.  Automatic Compositional Reasoning for Probabilistic Model Checking of Hardware Designs , 2010, 2010 Seventh International Conference on the Quantitative Evaluation of Systems.

[7]  Joost-Pieter Katoen,et al.  Counterexample Generation in Probabilistic Model Checking , 2009, IEEE Transactions on Software Engineering.

[8]  R. Milner,et al.  Bigraphical Reactive Systems , 2001, CONCUR.

[9]  Vincent D. Blondel,et al.  Undecidable Problems for Probabilistic Automata of Fixed Dimension , 2003, Theory of Computing Systems.

[10]  Christel Baier,et al.  Principles of model checking , 2008 .

[11]  Howard Barringer,et al.  Learning to divide and conquer: applying the L* algorithm to automate assume-guarantee reasoning , 2008, Formal Methods Syst. Des..

[12]  Amaury Habrard,et al.  A Polynomial Algorithm for the Inference of Context Free Languages , 2008, ICGI.

[13]  François Denis,et al.  Learning Classes of Probabilistic Automata , 2004, COLT.

[14]  Hongyang Qu,et al.  Assume-Guarantee Verification for Probabilistic Systems , 2010, TACAS.

[15]  Dana Angluin,et al.  Learning Regular Sets from Queries and Counterexamples , 1987, Inf. Comput..

[16]  Yih-Kuen Tsay,et al.  Automated Assume-Guarantee Reasoning through Implicit Learning , 2010, CAV.

[17]  Colin de la Higuera,et al.  Learning Stochastic Finite Automata , 2004, ICGI.

[18]  Marta Z. Kwiatkowska,et al.  PRISM 4.0: Verification of Probabilistic Real-Time Systems , 2011, CAV.

[19]  Joël Ouaknine,et al.  Language Equivalence for Probabilistic Automata , 2011, CAV.

[20]  Joël Ouaknine,et al.  On Probabilistic Program Equivalence and Refinement , 2005, CONCUR.

[21]  Roberto Segala,et al.  Modeling and verification of randomized distributed real-time systems , 1996 .

[22]  Azaria Paz,et al.  Probabilistic automata , 2003 .

[23]  J. Kemeny,et al.  Denumerable Markov chains , 1969 .

[24]  Christel Baier,et al.  Probabilistic ω-automata , 2012, JACM.

[25]  Francesco Bergadano,et al.  Learning Behaviors of Automata from Multiplicity and Equivalence Queries , 1994, SIAM J. Comput..

[26]  Thomas A. Henzinger,et al.  Equivalence of Labeled Markov Chains , 2008, Int. J. Found. Comput. Sci..

[27]  Wen-Guey Tzeng,et al.  A Polynomial-Time Algorithm for the Equivalence of Probabilistic Automata , 1992, SIAM J. Comput..

[28]  Wen-Guey Tzeng,et al.  Learning Probabilistic Automata and Markov Chains via Queries , 1992, Machine Learning.