Refining Interface Alphabets for Compositional Verification

Abstract

Techniques for learning automata have been adapted to automatically infer assumptions in assume-guarantee compositional verification. Learning, in this context, produces assumptions and modifies them using counterexamples obtained by model checking components separately. In this process, the interface alphabets between components, that constitute the alphabets of the assumption automata, are fixed: they include all actions through which the components communicate. This paper introduces alphabet refinement, a novel technique that extends the assumption learning process to also infer interface alphabets. The technique starts with only a subset of the interface alphabet and adds actions to it as necessary until a given property is shown to hold or to be violated in the system. Actions to be added are discovered by counterexample analysis. We show experimentally that alphabet refinement improves the current learning algorithms and makes compositional verification by learning assumptions more scalable than non-compositional verification.

Optimized L*-Based Assume-Guarantee Reasoning

“…An approach similar to our third optimization was proposed independently by Gheorghiu et. al [18]. However, they use polynomial (greedy) heuristics aimed at minimizing the alphabet size, whereas we find the optimal value, and hence we solve an NP-hard problem.…”

Learning Minimal Separating DFA’s for Compositional Verification

“…We implemented all of those algorithms, including the heuristic algorithm for minimizing a 3DFA. We did not consider optimization techniques such as alphabet refinement [6,12]. This is fair because such techniques can also be easily adapted to L Sep .…”

“…For the case where components and properties are given as regular languages, several automatic approaches have been proposed to find contextual assumptions [4,10] based on the machine learning algorithm L * [2,17]. Following this line of research, there have been results for symbolic implementations [1,18], various optimization techniques [12,6], an extension to liveness properties [11], performance evaluation [9], and applications to problems such as component substitutability analysis [5]. However, all of the above suffer from the same problem: they do not guarantee finding a small assumption even if one exists.…”

Learning Assumptions for CompositionalVerification of Timed Systems

“…This work is a pioneer of automating the untimed compositional verification based on learning techniques. Consequently, several improvements [9], [15], [35] have been proposed to further reduce the complexity. These improvements focus on reducing the size of the alphabet during learning, which dominates the time complexity of the membership query in the L * algorithm.…”

“…Gheorghiu et al [15] used the abstraction-refinement paradigm [11] to infer the necessary alphabet of the untimed assumption A for AGR. Howar et al [22] also used the paradigm on the alphabet for inferring abstract λ (a, xa = 3) λ 1 0 (s0) (a, xa = 0) 0 0 (s1) (a, xa = 1) 1 1 (s2) (a, xa = 2) 0 0 (a, xa = 3) 0 0 (a, xa ≥ 3) 0 0 (a, 0 ≤ xa ≤ 1) 0 0 (a, 1 ≤ xa ≤ 2) 0 0 (a, 2 ≤ xa ≤ 3) 0 0 (a, 0 ≤ xa ≤ 2) 0 0 (a, 1 ≤ xa ≤ 3) 0 0 (a, 0 ≤ xa ≤ 3) 0 0 (a, xa = 0)(a, xa = 0) 0 0 (a, xa = 0)(a, xa = 1) 0 0 (a, xa = 0)(a, xa = 2) 0 0 (a, xa = 0)(a, xa = 3) 0 0 (a, xa = 0)(a, xa ≥ 3) 0 0 (a, xa = 0)(a, 0 ≤ xa ≤ 1) 0 0 (a, xa = 0)(a, 1 ≤ xa ≤ 2) 0 0 (a, xa = 0)(a, 2 ≤ xa ≤ 3) 0 0 (a, xa = 0)(a, 0 ≤ xa ≤ 2) 0 0 (a, xa = 0)(a, 1 ≤ xa ≤ 3) 0 0 (a, xa = 0)(a, 0 ≤ xa ≤ 3) 0 0 (a, xa = 1)(a, xa = 0) 0 0 (a, xa = 1)(a, xa = 1) 0 0 (a, xa = 1)(a, xa = 2) 0 0 (a, xa = 1)(a, xa = 3) 1 0 (a, xa = 1)(a, xa ≥ 3) 0 0 (a, xa = 1)(a, 0 ≤ xa ≤ 1) 0 0 (a, xa = 1)(a, 1 ≤ xa ≤ 2) 0 0 (a, xa = 1)(a, 2 ≤ xa ≤ 3) 0 0 (a, xa = 1)(a, 0 ≤ xa ≤ 2) 0 0 (a, xa = 1)(a, 1 ≤ xa ≤ 3) 0 0 (a, xa = 1)(a, 0 ≤ xa ≤ 3) 0 0 Table Constructed by TL * sg automata with respect to given concrete behavior such that determinism is preserved.…”