Significant Diagnostic Counterexamples in Probabilistic Model Checking
This paper presents a novel technique for counterexample generation in probabilistic model checking of Markov chains and Markov Decision Processes. (Finite) paths in counterexamples are grouped together in witnesses that are likely to provide similar debugging information to the user. We list five properties that witnesses should satisfy in order to be useful as debugging aid: similarity, accuracy, originality, significance, and finiteness. Our witnesses contain paths that behave similarly outside strongly connected components.
Then, we show how to compute these witnesses by reducing the problem of generating counterexamples for general properties over Markov Decision Processes, in several steps, to the easy problem of generating counterexamples for reachability properties over acyclic Markov chains.
KeywordsMarkov Chain Model Check Markov Decision Process Linear Temporal Logic Propositional Formula
Unable to display preview. Download preview PDF.
- [AD06]Andrés, M.E., D’Argenio, P.: Derivation of counterexamples for quanti- tative model checking. Master’s thesis, Universidad Nacional de Córdoba (2006)Google Scholar
- [AL07]Aljazzar, H., Leue, S.: Counterexamples for model checking of markov decision processes. Computer Science Technical Report soft-08-01, University of Konstanz (December 2007)Google Scholar
- [Alf97]De Alfaro, L.: Temporal logics for the specification of performance and reliability, pp. 165–176. Springer, Heidelberg (1997)Google Scholar
- [Cas93]Cassandras, C.G.: Discrete Event Systems: Modeling and Performance Analysis. Richard D. Irwin, Inc./Aksen Associates, Inc. (1993)Google Scholar
- [CGJ+00]Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Computer Aided Verification, pp. 154–169 (2000)Google Scholar
- [dA97]de Alfaro, L.: Formal Verification of Probabilistic Systems. Ph.D thesis, Stanford University (1997)Google Scholar
- [Epp98]Eppstein, D.: Finding the k shortest paths. SIAM Journal of Computing, 652–673 (1998)Google Scholar
- [FV97]Filar, J., Vrieze, K.: Competitive Markov Decision Processes (1997)Google Scholar
- [Var85]Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state systems. In: Proc. 26th IEEE Symp. Found. Comp. Sci., pp. 327–338 (1985)Google Scholar