Counterexample Generation for Discrete-Time Markov Chains Using Bounded Model Checking

Counterexamples in Probabilistic LTL Model Checking for Markov Chains

“…This raises the question of how the user can understand what words are contained in W . Also, the reader may want evidence that indeed P [W ↑] ≥ t. Similar questions arise in the study of counterexamples for probabilistic CTL ( [14]) model checking, and we refer to the literature for possible approaches [4,5,9,23]. We also discuss these issues further in Section 6.…”

“…Aljazzar and Leue [2] propose solutions for counterexamples in probabilistic model checking with respect to timed probabilistic reachability properties in Markov chains. Han and Katoen [12] and Wimmer et al [23] present algorithms computing counterexamples for model checking PCTL (probabilistic CTL [14]) formulas in Markov chains. There are also suggestions of how to present such counterexamples to the user [4,9].…”

Minimal Critical Subsystems for Discrete-Time Markov Models

“…Therefore, in recent years much research effort has been made to develop algorithms for counterexample generation for DTMCs and MDPs (see, e. g., [5][6][7][8][9][10][11][12][13]). Most of these algorithms [6][7][8][9] yield path-based counterexamples, i. e., counterexamples in the form of a set of finite paths that all lead from the initial state to a safety-critical state and whose joint probability mass exceeds the allowed limit.…”

“…The size of the counterexample may be several orders of magnitude larger than the number of system states, rendering the counterexample practically unusable for debugging purposes. Different proposals have been made to alleviate this problem: [6] represents the path set as a regular expression, [7] detects loops on paths, and [8] shrinks paths through strongly connected components into single transitions.…”

Diagnosis, synthesis and analysis of probabilistic models

“…Wimmer, Braitling and Becker [WBB09] proposed to apply bounded model checking to generate counterexamples for DTMCs. Novel optimization techniques like loop-detection are applied not only to speed up the counterexample computation, but also to reduce the size of the counterexamples significantly.…”