1,843 research outputs found
A Survey of Satisfiability Modulo Theory
Satisfiability modulo theory (SMT) consists in testing the satisfiability of
first-order formulas over linear integer or real arithmetic, or other theories.
In this survey, we explain the combination of propositional satisfiability and
decision procedures for conjunctions known as DPLL(T), and the alternative
"natural domain" approaches. We also cover quantifiers, Craig interpolants,
polynomial arithmetic, and how SMT solvers are used in automated software
analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest,
Romania. 201
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
A Logical Approach to Efficient Max-SAT solving
Weighted Max-SAT is the optimization version of SAT and many important
problems can be naturally encoded as such. Solving weighted Max-SAT is an
important problem from both a theoretical and a practical point of view. In
recent years, there has been considerable interest in finding efficient solving
techniques. Most of this work focus on the computation of good quality lower
bounds to be used within a branch and bound DPLL-like algorithm. Most often,
these lower bounds are described in a procedural way. Because of that, it is
difficult to realize the {\em logic} that is behind.
In this paper we introduce an original framework for Max-SAT that stresses
the parallelism with classical SAT. Then, we extend the two basic SAT solving
techniques: {\em search} and {\em inference}. We show that many algorithmic
{\em tricks} used in state-of-the-art Max-SAT solvers are easily expressable in
{\em logic} terms with our framework in a unified manner.
Besides, we introduce an original search algorithm that performs a restricted
amount of {\em weighted resolution} at each visited node. We empirically
compare our algorithm with a variety of solving alternatives on several
benchmarks. Our experiments, which constitute to the best of our knowledge the
most comprehensive Max-sat evaluation ever reported, show that our algorithm is
generally orders of magnitude faster than any competitor
Learning for Dynamic subsumption
In this paper a new dynamic subsumption technique for Boolean CNF formulae is
proposed. It exploits simple and sufficient conditions to detect during
conflict analysis, clauses from the original formula that can be reduced by
subsumption. During the learnt clause derivation, and at each step of the
resolution process, we simply check for backward subsumption between the
current resolvent and clauses from the original formula and encoded in the
implication graph. Our approach give rise to a strong and dynamic
simplification technique that exploits learning to eliminate literals from the
original clauses. Experimental results show that the integration of our dynamic
subsumption approach within the state-of-the-art SAT solvers Minisat and Rsat
achieves interesting improvements particularly on crafted instances
On Different Strategies for Eliminating Redundant Actions from Plans
Satisficing planning engines are often able to generate plans in a reasonable time, however, plans are often far from optimal. Such plans often contain a high number of redundant actions, that are actions, which can be removed without affecting the validity of the plans. Existing approaches for determining and eliminating redundant actions work in polynomial time, however, do not guarantee eliminating the "best" set of redundant actions, since such a problem is NP-complete. We introduce an approach which encodes the problem of determining the "best" set of redundant actions (i.e. having the maximum total-cost) as a weighted MaxSAT problem. Moreover, we adapt the existing polynomial technique which greedily tries to eliminate an action and its dependants from the plan in order to eliminate more expensive redundant actions. The proposed approaches are empirically compared to existing approaches on plans generated by state-of-the-art planning engines on standard planning benchmark
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