Boosting interpolation with dynamic localized abstraction and redundancy removal

Abstract

SAT-based Unbounded Model Checking based on Craig Interpolants is often able to overcome BDDs and other SAT-based techniques on large verification instances. Based on refutation proofs generated by SAT solvers, interpolants provide compact circuit representations of state sets, as they abstract away several nonrelevant details of the proofs. We propose three main contributions, aimed at controlling interpolant size and traversal depth. First of all, we introduce interpolant-based dynamic abstraction to reduce the support of computed interpolants. Subsequently, we propose new advances in interpolant compaction by redundancy removal. Finally, we introduce interpolant computation exploiting circuit quantification, instead of SAT refutation proofs. These techniques heavily rely on an effective application of the incremental SAT paradigm. The experimental results proposed in this paper are specifically oriented to prove properties, rather than disproving them, i.e., they target complete verification instead of simply hunting bugs. They show how this methodology is able to stretch the applicability of interpolant-based Model Checking to larger and deeper verification instances.

Secure embedded architectures: Taint properties verification

“…• BDD-based representations and traversals (BDD), including forward, backward, combined (approximate) forward/ (exact) backward reachability algorithms [14], [15] partitioned BDDs and/or image computation procedures [16], [17] • Interpolant-based verification (ITP), with ad-hoc abstraction and tightening techniques [18], [19], integrated SAT-based approaches [20], [21], Interpolant reduction techniques [22] and Guided Refinement [23] • Property Directed Reachability (PDR) verification strategies [24] Figures 4 and 5 show verification results considering three different unbounded model checking strategies: interpolation (ITP), binary decision diagram reachability (BDD) and Property Directed Reachability strategy (PDR). Results show that the most suitable strategy for the presented security properties verification is PDR.…”

Benchmarking a model checker for algorithmic improvements and tuning for performance

“…This work led us to consider 11 new engines, and enrich our portfolio, to finally include the following 36 methodologies: -9 BDD-based methods [12], i.e., forward, backward and forward/backward, with 3 MC schemes available for each method, based on different clustering and early quantification, insertion of cut-point, etc. -24 ITP-based [16] techniques, with different partitioning and quantification schemes [17][18][19][20][21] (6 base engines multiplied by 4 different running configurations). -2 SAT-based strategies (simple induction [14] and inductive invariants [15,22]).…”

“…-Interpolant-based verification, with ad-hoc abstraction and tightening techniques [18,19], integrated SAT-based approaches [20,21]. -Inductive reasoning (inductive invariants [22,30]) and symbolic manipulation of AndInvert Graphs (AIGs [31]), with circuit-based quantification [32].…”

“…Affinity is also kept High with Long runs, in case of quick interpolant computation. Tuning is possibly moved to Aggressive, either for more compaction effort, or to select different overall strategies (e.g., dynamic abstraction [18,19]). Affinity changes to Low when both SAT calls and interpolants become difficult.…”

Optimization techniques for craig interpolant compaction in unbounded model checking

“…Whereas one of their major challenges is the inherent redundancy of interpolant circuits, as well as the need for fast and scalable techniques to compact them. Improvements over the base method [3] were proposed in [6][7][8][9] and [10,11], in order to push forward applicability and scalability of the technique.…”