Learning Minimal Separating DFA’s for Compositional Verification

Abstract

Abstract. Algorithms for learning a minimal separating DFA of two disjoint regular languages have been proposed and adapted for different applications. One of the most important applications is learning minimal contextual assumptions in automated compositional verification. We propose in this paper an efficient learning algorithm, called L Sep , that learns and generates a minimal separating DFA. Our algorithm has a quadratic query complexity in the product of sizes of the minimal DFA's for the two input languages. In contrast, the most recent algorithm of Gupta et al. has an exponential query complexity in the sizes of the two DFA's. Moreover, experimental results show that our learning algorithm significantly outperforms all existing algorithms on randomly-generated example problems. We describe how our algorithm can be adapted for automated compositional verification. The adapted version is evaluated on the LTSA benchmarks and compared with other automated compositional verification approaches. The result shows that our algorithm surpasses others in 30 of 49 benchmark problems.

Automated Learning of Probabilistic Assumptions for Compositional Reasoning

“…There have been several attempts to improve performance, including symbolic implementations [31] and optimisations to the use of L* [9]. Others have also devised alternative learning-based methods, for example by reformulating the assumption generation problem as one of computing the smallest finite automaton separating two regular languages [23,11], or using the CDNF learning algorithm to generate implicit representations of assumptions [10].…”

Automated Circular Assume-Guarantee Reasoning

“…Previous work used approximate iterative techniques based on automata learning or abstraction refinement to automate the assumption generation in the context of acyclic rules [7,19,3,4,2,5,6]. A different approach [10] used a SAT solver over a set of constraints encoding how the assumptions should be updated to find minimal assumptions; the method was shown to work well in practice, in the context of the same acyclic rule.…”

“…Progress has been made on automating compositional reasoning using learning and abstraction-refinement techniques for iterative building of the necessary assumptions [7,19,3,4,2,5,6]. This work has been done mostly in the context of applying a simple compositional assume-guarantee rule, where assumptions and properties are related in an acyclic manner.…”

Random Generation of Deterministic Tree (Walking) Automata

“…2 The random generation of non deterministic finite word automata is still mostly open. Two recent papers propose such random generation algorithms: Tabakov and Vardi [13] apply theirs to the evaluation of inclusion testing procedures, whereas Chen et al [7] evaluate the performance of a learning algorithm. Both algorithms are ad hoc and fail to provide statistically exploitable distributions.…”