Counterexample Generation in Stochastic Model Checking Based on PSO Algorithm with Heuristic

Abstract

Providing counterexample for the refutation of a property is an essential feature of model checking, if it is not the most important. However, generating counterexample in stochastic model checking needs a dedicated algorithm. It usually costs too much time and memory, and sometimes it cannot find the counterexample. What is worse, generating smallest counterexample in stochastic model checking has been proved to be NP-complete, and it is unlikely to be efficiently approximable. Although there are a few heuristic methods that are applied to the construction of the counterexample, it is usually difficult to determine the heuristic function which is critical for counterexample generating. In this paper, we present a particle swarm optimization (PSO)-based approach to generating counterexample for stochastic model checking. We define the diagnostic sub-graph as counterexample, and extend PSO algorithm with heuristic (HPSO) to generate counterexample. It adopts indirect path coding scheme to expand the scope of the search space, and employs heuristic operator to generate more effective path. The validity of our approach is illustrated by some case studies in a prototype tool. The experiments show that HPSO algorithm can significantly outperform the present algorithm for counterexample generation in stochastic model checking.

Compositional Stochastic Model Checking Probabilistic Automata via Assume-guarantee Reasoning

“…We use PRISM [25] and counterexample construction algorithm (i.e., particle swarm optimization algorithm [40]) to form a MAT. Then through the libalf [41] learning library, we can implement the NL* algorithm and pose membership and equivalence queries to a MAT.…”

“…Through a multi-objective model checking technique [18,33], we can calculate the probability of a conjectured assumption, which is an interval I A1 . If I A1 is an empty interval, the framework will construct a probabilistic counterexample cex(s, w, c [22] and Ma et al [40]. Next, we must check whether the appearance of a trace t 1 in the probabilistic counterexample cex(s, w, c) causes the violation of 〈P〉 ≥PG on M 1 ||M 2 .…”

“…Since P 1 * P 2 = 0.2 * 0.1 > (1 − 0.99) = 0.01, 〈shutdown〉 is a counterexample c of the target language ℒ(M 1 ||M 2 ), the learning algorithm is terminated and returns the probabilistic counterexample trace cex(0.02, 〈shutdown〉). We can construct a probabilistic counterexample cex(s, w, c) [22,40] Figure 4.…”

A Probabilistic Assume-Guarantee Reasoning Framework Based on Genetic Algorithm

“…We construct the assumption with a small subset of the interface alphabet, and add actions to the necessary alphabet until the required property is shown to be hold or violated in the system, which are decided by counterexample analysis. Moreover, we employ the diagnostic submodel [24] as counterexample for guidance of training set augment. It will be useful for reducing time consumption of assumption generation.…”

“…It will be useful for reducing time consumption of assumption generation. We solve PAG problem in the following way: (a) generate assumption from MDP interface alphabet by a genetic algorithm; (b) use multi-objective stochastic model checking technique to checking the assumeguarantee tuple; (c) adopt the method of reference [24] to construct the counterexample.…”