Vadim Ryvchin

Efficient MUS extraction with resolution

We report advances in state-of-the-art algorithms for the problem of Minimal Unsatisfiable Subformula (MUS) extraction. First, we demonstrate how to apply techniques used in the past to speed up resolution-based Group MUS extraction to plain MUS extraction. Second, we show that model rotation, presented in the context of assumption-based MUS extraction, can also be used with resolution-based MUS extraction. Third, we introduce an improvement to rotation, called eager rotation. Finally, we propose a new technique for speeding-up resolution-based MUS extraction, called path strengthening. We integrated the above techniques into the publicly available resolution-based MUS extractor HaifaMUC, which, as a result, now outperforms leading MUS extractors.

Efficient SAT solving under assumptions

In incremental SAT solving, assumptions are propositions that hold solely for one specific invocation of the solver. Effective propagation of assumptions is vital for ensuring SAT solving efficiency in a variety of applications. We propose algorithms to handle assumptions. In our approach, assumptions are modeled as unit clauses, in contrast to the current state-of-the-art approach that models assumptions as first decision variables. We show that a notable advantage of our approach is that it can make preprocessing algorithms much more effective. However, our initial scheme renders assumption-dependent (or temporary) conflict clauses unusable in subsequent invocations. To resolve the resulting problem of reduced learning power, we introduce an algorithm that transforms such temporary clauses into assumption-independent pervasive clauses. In addition, we show that our approach can be enhanced further when a limited form of look-ahead information is available. We demonstrate that our approach results in a considerable performance boost of the SAT solver on instances generated by a prominent industrial application in hardware validation.

Ultimately Incremental SAT

Incremental SAT solving under assumptions, introduced in Minisat, is in wide use. However, Minisat’s algorithm for incremental SAT solving under assumptions has two main drawbacks which hinder performance considerably. First, it is not compliant with the highly effective and commonly used preprocessor SatELite. Second, all the assumptions are left in the formula, rather than being represented as unit clauses, propagated, and eliminated. Two previous attempts to overcome these problems solve either the first or the second of them, but not both. This paper remedies this situation by proposing a comprehensive solution for incremental SAT solving under assumptions, where SatELite is applied and all the assumptions are propagated. Our algorithm outperforms existing approaches over publicly available instances generated by a prominent industrial application in hardware validation.

Assignment stack shrinking

Assignment stack shrinking is a technique that is intended to speed up the performance of modern complete SAT solvers. Shrinking was shown to be efficient in SAT’04 competition winners Jerusat and Chaff. However, existing studies lack the details of the shrinking algorithm. In addition, shrinking’s performance was not tested in conjunction with the most modern techniques. This paper provides a detailed description of the shrinking algorithm and proposes two new heursitics for it. We show that using shrinking is critical for solving well-known industrial benchmark families with the latest versions of Minisat and Eureka.

Bit-Vector Optimization

A variety of applications of Satisfiability Modulo Theories SMT require finding a satisfying assignment which optimizes some user-given function. Optimization in the context of SMT is referred to as Optimization Modulo Theories OMT. Current OMT research is mostly dedicated to optimization in arithmetic domains. This paper is about Optimization modulo Bit-Vectors OBV. We introduce two OBV algorithms which can easily be implemented in an eager bit-vector solver. We show that an industrial problem of fixing cell placement during the physical design stage of the CAD process can be reduced to optimization modulo either Bit-Vectors BV or Linear Integer Arithmetic LIA. We demonstrate that our resulting OBV tool can solve industrial instances which are out of reach of existing BV and LIA OMT solvers.

Preprocessing in incremental SAT

Preprocessing of CNF formulas is an invaluable technique when attempting to solve large formulas, such as those that model industrial verification problems. Unfortunately, the best combination of preprocessing techniques, which involve variable elimination combined with subsumption, is incompatible with incremental satisfiability. The reason is that soundness is lost if a variable is eliminated and later reintroduced. Look-ahead is a known technique to solve this problem, which simply blocks elimination of variables that are expected to be part of future instances. The problem with this technique is that it relies on knowing the future instances, which is impossible in several prominent domains. We show a technique for this realm, which is empirically far better than the known alternatives: running without preprocessing at all or applying preprocessing separately at each step.

Mining Backbone Literals in Incremental SAT

In incremental SAT solving, information gained from previous similar instances has so far been limited to learned clauses that are still relevant, and heuristic information such as activity weights and scores. In most settings in which incremental satisfiability is applied, many of the instances along the sequence of formulas being solved are unsatisfiable. We show that in such cases, with a P-time analysis of the proof, we can compute a set of literals that are logically implied by the next instance. By adding those literals as assumptions, we accelerate the search.

Efficient generation of small interpolants in CNF

Interpolation-based model checking (ITP) McMillan (in CAV, 2003) is an efficient and complete model checking procedure. However, for large problems, interpolants generated by ITP might become extremely large, rendering the procedure slow or even intractable. In this work we present a novel technique for interpolant generation in the context of model checking. The main novelty of our work is that we generate small interpolants in conjunctive normal form (CNF) using a twofold procedure: first we propose an algorithm that exploits resolution refutation properties to compute an interpolant approximation. Then we introduce an algorithm that takes advantage of inductive reasoning to turn the interpolant approximation into an interpolant. Unlike ITP, our approach maintains only the relevant subset of the resolution refutation. In addition, the second part of the procedure exploits the properties of the model checking problem at hand, in contrast to the general-purpose algorithm used in ITP. We developed a new interpolation-based model checking algorithm, called CNF-ITP. Our algorithm takes advantage of the smaller interpolants and exploits the fact that the interpolants are given in CNF. We integrated our method into a SAT-based model checker and experimented with a representative subset of the HWMCC’12 benchmark set. Our experiments show that, overall, the interpolants generated by our method are 117 times smaller than those generated by ITP. Our CNF-ITP algorithm outperforms ITP, and at times solves problems that ITP cannot solve. We also compared CNF-ITP to the successful IC3 Bradely (in VMCAI, volume 6538 of lecture notes in computer science, 2011) algorithm. We found that CNF-ITP outperforms IC3 Bradely (in VMCAI, volume 6538 of lecture notes in computer science, 2011) in a large number of cases.