Core Minimization in SAT-based Abstraction

Abstract

Abstract-Automatic abstraction is an important component of modern formal verification flows. A number of effective SATbased automatic abstraction methods use unsatisfiable cores to guide the construction of abstractions. In this paper we analyze the impact of unsatisfiable core minimization, using state-ofthe-art algorithms for the computation of minimally unsatisfiable subformulas (MUSes), on the effectiveness of a hybrid (counterexample-based and proof-based) abstraction engine. We demonstrate empirically that core minimization can lead to a significant reduction in the total verification time, particularly on difficult testcases. However, the resulting abstractions are not necessarily smaller. We notice that by varying the minimization effort the abstraction size can be controlled in a non-trivial manner. Based on this observation, we achieve a further reduction in the total verification time.

Accelerated Deletion-based Extraction of Minimal Unsatisfiable Cores

“…Convert the implication of l into a decision, and update accordingly the decision level of all implied literals in the trail that come after it. 4. Call Analyze Conflict() with the same conflicting clause, but while referring to the new decision levels.…”

“…The problem for finding a small, a minimal (irreducible), the minimum (smallest minimal), or all the MUCs has been addressed frequently over the last decade [51,19,9,36,28,49,17,13,42,8,1,27,46,18,20,38,14,26,50,33,43,12,41,6,30,7,48,5,4,29,24,35,39] because of its theoretical and practical importance. The applications of MUC-extraction include abstraction refinement for model checking [31,21,4], formal equivalence verification [23,12] and functional bi-composition [25,10] -see [43,34] for extensive surveys.…”