Counterexamples for Timed Probabilistic Reachability

Abstract

Abstract. The inability to provide counterexamples for the violation of timed probabilistic reachability properties constrains the practical use of CSL model checking for continuous time Markov chains (CTMCs). Counterexamples are essential tools in determining the causes of property violations and are required during debugging. We propose the use of explicit state model checking to determine runs leading into property offending states. Since we are interested in finding paths that carry large amounts of probability mass we employ directed explicit state model checking technology to find such runs using a variety of heuristics guided search algorithms, such as Best First search and Z*. The estimates used in computing the heuristics rely on a uniformisation of the CTMC. We apply our approach to a probabilistic model of the SCSI-2 protocol.

Counterexamples in Probabilistic Model Checking

“…The SE problem for timed reachability in CTMCs is considered in [3]. Whereas we consider the generation of strongest evidences once a property violation has been established, [3] assumes the CTMC to be unknown.…”

“…The SE problem for timed reachability in CTMCs is considered in [3]. Whereas we consider the generation of strongest evidences once a property violation has been established, [3] assumes the CTMC to be unknown. The SE problem for CTMCs is mapped onto an SE problem on (uniformised) DTMCs, and heuristic search algorithms (Z * ) are employed to determine the evidences.…”

“…In probabilistic model checking, however, counterexample generation is almost not developed; notable exception is the recent heuristic search algorithm for CTMCs and DTMCs [3,4] that works under the assumption that the model is unknown. Instead, we consider a setting in which it has already been established that a certain state refutes a given property.…”

Significant Diagnostic Counterexamples in Probabilistic Model Checking

“…Presently, some work has been done on counterexample generation techniques for different variants of probabilistic models (Discrete Markov chains and Continues Markov chains) [AHL05,AL06,HK07a,HK07b]. In our terminology, these works consider witnesses consisting of a single finite path.…”

Diagnosis, synthesis and analysis of probabilistic models

“…Aljazzar and Leue investigated to apply directed explicit state space search to counterexample generation in DTMC and CTMC model checking of PCTL and CSL properties in [AHL05][AL06]. The presented search algorithms can explore the state space on the fly and can be further guided by heuristics to improve the performance of the algorithm.…”