Implication-Based Approximating Bounded Model Checking

Abstract

Abstract. This paper presents an iterative framework based on overapproximation and under-approximation for traditional bounded model checking (BMC). A novel feature of our approach is the approximations are defined based on "implication" instead of "simulation". As a common partial order relation of logic formulas, implication is suitable for the satisfiability checking of BMC for debugging. Our approach could generate the implication-based approximations efficiently with necessary accuracy, thus it potentially enables BMC to go deeper and the output counterexamples with fewer variables are easier to understand. An experiment on a suite of Petri nets shows the effectiveness of implication-based approximating BMC.

变量极小公式复杂性

“…化为逻辑公式的性质判定, 如等价性判定、可满足性 判定等 [1] . 对逻辑公式在保持特定性质的前提下进行 化简, 不但能够降低应用问题的求解复杂度, 同时也 能够为应用系统的错误定位和故障调试提供更为准 确的信息 [2] .…”

The complexity of variable minimal formulas

“…Due to the limit ation of space, it is demanded that logic formulas should be represented in a concise way. The task of debugging and fault localization of applications is facilitated with small logic formulas [2]. This motivates us to consider a small formula with fewer variables, namely variable minimal formulas in this paper.…”