Proceedings of the 2010 ICSE Workshop on Quantitative Stochastic Models in the Verification and Design of Software Systems
A game-based abstraction-refinement framework for Markov decision processes
Formal Methods in System Design
YAGA: automated analysis of quantitative safety specifications in probabilistic B
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
Automated learning of probabilistic assumptions for compositional reasoning
FASE'11/ETAPS'11 Proceedings of the 14th international conference on Fundamental approaches to software engineering: part of the joint European conferences on theory and practice of software
Counterexample generation for Markov chains using SMT-based bounded model checking
FMOODS'11/FORTE'11 Proceedings of the joint 13th IFIP WG 6.1 and 30th IFIP WG 6.1 international conference on Formal techniques for distributed systems
DiPro: a tool for probabilistic counterexample generation
Proceedings of the 18th international SPIN conference on Model checking software
From probabilistic counterexamples via causality to fault trees
SAFECOMP'11 Proceedings of the 30th international conference on Computer safety, reliability, and security
Hierarchical counterexamples for discrete-time Markov chains
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Learning-based compositional verification for synchronous probabilistic systems
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Minimal critical subsystems for discrete-time markov models
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
The COMICS tool: computing minimal counterexamples for DTMCs
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Refinement and difference for probabilistic automata
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
High-Level counterexamples for probabilistic automata
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
Effective verification of confidentiality for multi-threaded programs
Journal of Computer Security - Foundational Aspects of Security
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Providing evidence for the refutation of a property is an essential, if not the most important, feature of model checking. This paper considers algorithms for counterexample generation for probabilistic CTL formulae in discrete-time Markov chains. Finding the strongest evidence (i.e., the most probable path) violating a (bounded) until-formula is shown to be reducible to a single-source (hop-constrained) shortest path problem. Counterexamples of smallest size that deviate most from the required probability bound can be obtained by applying (small amendments to) k-shortest (hop-constrained) paths algorithms. These results can be extended to Markov chains with rewards, to LTL model checking, and are useful for Markov decision processes. Experimental results show that typically the size of a counterexample is excessive. To obtain much more compact representations, we present a simple algorithm to generate (minimal) regular expressions that can act as counterexamples. The feasibility of our approach is illustrated by means of two communication protocols: leader election in an anonymous ring network and the Crowds protocol.