1,704 research outputs found
On Tackling the Limits of Resolution in SAT Solving
The practical success of Boolean Satisfiability (SAT) solvers stems from the
CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a
propositional proof complexity perspective, CDCL is no more powerful than the
resolution proof system, for which many hard examples exist. This paper
proposes a new problem transformation, which enables reducing the decision
problem for formulas in conjunctive normal form (CNF) to the problem of solving
maximum satisfiability over Horn formulas. Given the new transformation, the
paper proves a polynomial bound on the number of MaxSAT resolution steps for
pigeonhole formulas. This result is in clear contrast with earlier results on
the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper
also establishes the same polynomial bound in the case of modern core-guided
MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard
for CDCL SAT solvers, show that these can be efficiently solved with modern
MaxSAT solvers
The Challenge of Unifying Semantic and Syntactic Inference Restrictions
While syntactic inference restrictions don't play an important role for SAT, they are an essential reasoning technique for more expressive logics, such as first-order logic, or fragments thereof. In particular, they can result in short proofs or model representations. On the other hand, semantically guided inference systems enjoy important properties, such as the generation of solely non-redundant clauses. I discuss to what extend the two paradigms may be unifiable
On Optimization Modulo Theories, MaxSMT and Sorting Networks
Optimization Modulo Theories (OMT) is an extension of SMT which allows for
finding models that optimize given objectives. (Partial weighted) MaxSMT --or
equivalently OMT with Pseudo-Boolean objective functions, OMT+PB-- is a
very-relevant strict subcase of OMT. We classify existing approaches for MaxSMT
or OMT+PB in two groups: MaxSAT-based approaches exploit the efficiency of
state-of-the-art MAXSAT solvers, but they are specific-purpose and not always
applicable; OMT-based approaches are general-purpose, but they suffer from
intrinsic inefficiencies on MaxSMT/OMT+PB problems.
We identify a major source of such inefficiencies, and we address it by
enhancing OMT by means of bidirectional sorting networks. We implemented this
idea on top of the OptiMathSAT OMT solver. We run an extensive empirical
evaluation on a variety of problems, comparing MaxSAT-based and OMT-based
techniques, with and without sorting networks, implemented on top of
OptiMathSAT and {\nu}Z. The results support the effectiveness of this idea, and
provide interesting insights about the different approaches.Comment: 17 pages, submitted at Tacas 1
Integrating Conflict Driven Clause Learning to Local Search
This article introduces SatHyS (SAT HYbrid Solver), a novel hybrid approach
for propositional satisfiability. It combines local search and conflict driven
clause learning (CDCL) scheme. Each time the local search part reaches a local
minimum, the CDCL is launched. For SAT problems it behaves like a tabu list,
whereas for UNSAT ones, the CDCL part tries to focus on minimum unsatisfiable
sub-formula (MUS). Experimental results show good performances on many classes
of SAT instances from the last SAT competitions
Optimization Modulo Theories with Linear Rational Costs
In the contexts of automated reasoning (AR) and formal verification (FV),
important decision problems are effectively encoded into Satisfiability Modulo
Theories (SMT). In the last decade efficient SMT solvers have been developed
for several theories of practical interest (e.g., linear arithmetic, arrays,
bit-vectors). Surprisingly, little work has been done to extend SMT to deal
with optimization problems; in particular, we are not aware of any previous
work on SMT solvers able to produce solutions which minimize cost functions
over arithmetical variables. This is unfortunate, since some problems of
interest require this functionality.
In the work described in this paper we start filling this gap. We present and
discuss two general procedures for leveraging SMT to handle the minimization of
linear rational cost functions, combining SMT with standard minimization
techniques. We have implemented the procedures within the MathSAT SMT solver.
Due to the absence of competitors in the AR, FV and SMT domains, we have
experimentally evaluated our implementation against state-of-the-art tools for
the domain of linear generalized disjunctive programming (LGDP), which is
closest in spirit to our domain, on sets of problems which have been previously
proposed as benchmarks for the latter tools. The results show that our tool is
very competitive with, and often outperforms, these tools on these problems,
clearly demonstrating the potential of the approach.Comment: Submitted on january 2014 to ACM Transactions on Computational Logic,
currently under revision. arXiv admin note: text overlap with arXiv:1202.140
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