13,650 research outputs found
Probing-Based Preprocessing Techniques for Propositional Satisfiability
Preprocessing is an often used approach for solving hard instances of propositional satisfiability (SAT). Preprocessing can be used for reducing the number of variables and for drastically modifying the set of clauses, either by eliminating irrelevant clauses or by inferring new clauses. Over the years, a large number of formula manipulation techniques has been proposed, that in some situations have allowed solving instances not otherwise solvable with stateof -the-art SAT solvers. This paper proposes probing-based preprocessing, an integrated approach for preprocessing propositional formulas, that for the first time integrates in a single algorithm most of the existing formula manipulation techniques. Moreover, the new unified framework can be used to develop new techniques. Preliminary experimental results illustrate that probing-based preprocessing can be effectively used as a preprocessing tool in state-of-theart SAT solvers
SAT-based Explicit LTL Reasoning
We present here a new explicit reasoning framework for linear temporal logic
(LTL), which is built on top of propositional satisfiability (SAT) solving. As
a proof-of-concept of this framework, we describe a new LTL satisfiability
tool, Aalta\_v2.0, which is built on top of the MiniSAT SAT solver. We test the
effectiveness of this approach by demonnstrating that Aalta\_v2.0 significantly
outperforms all existing LTL satisfiability solvers. Furthermore, we show that
the framework can be extended from propositional LTL to assertional LTL (where
we allow theory atoms), by replacing MiniSAT with the Z3 SMT solver, and
demonstrating that this can yield an exponential improvement in performance
SAT Solving for Argument Filterings
This paper introduces a propositional encoding for lexicographic path orders
in connection with dependency pairs. This facilitates the application of SAT
solvers for termination analysis of term rewrite systems based on the
dependency pair method. We address two main inter-related issues and encode
them as satisfiability problems of propositional formulas that can be
efficiently handled by SAT solving: (1) the combined search for a lexicographic
path order together with an \emph{argument filtering} to orient a set of
inequalities; and (2) how the choice of the argument filtering influences the
set of inequalities that have to be oriented. We have implemented our
contributions in the termination prover AProVE. Extensive experiments show that
by our encoding and the application of SAT solvers one obtains speedups in
orders of magnitude as well as increased termination proving power
Set Constraint Model and Automated Encoding into SAT: Application to the Social Golfer Problem
On the one hand, Constraint Satisfaction Problems allow one to declaratively
model problems. On the other hand, propositional satisfiability problem (SAT)
solvers can handle huge SAT instances. We thus present a technique to
declaratively model set constraint problems and to encode them automatically
into SAT instances. We apply our technique to the Social Golfer Problem and we
also use it to break symmetries of the problem. Our technique is simpler, more
declarative, and less error-prone than direct and improved hand modeling. The
SAT instances that we automatically generate contain less clauses than improved
hand-written instances such as in [20], and with unit propagation they also
contain less variables. Moreover, they are well-suited for SAT solvers and they
are solved faster as shown when solving difficult instances of the Social
Golfer Problem.Comment: Submitted to Annals of Operations researc
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
Stable Model Counting and Its Application in Probabilistic Logic Programming
Model counting is the problem of computing the number of models that satisfy
a given propositional theory. It has recently been applied to solving inference
tasks in probabilistic logic programming, where the goal is to compute the
probability of given queries being true provided a set of mutually independent
random variables, a model (a logic program) and some evidence. The core of
solving this inference task involves translating the logic program to a
propositional theory and using a model counter. In this paper, we show that for
some problems that involve inductive definitions like reachability in a graph,
the translation of logic programs to SAT can be expensive for the purpose of
solving inference tasks. For such problems, direct implementation of stable
model semantics allows for more efficient solving. We present two
implementation techniques, based on unfounded set detection, that extend a
propositional model counter to a stable model counter. Our experiments show
that for particular problems, our approach can outperform a state-of-the-art
probabilistic logic programming solver by several orders of magnitude in terms
of running time and space requirements, and can solve instances of
significantly larger sizes on which the current solver runs out of time or
memory.Comment: Accepted in AAAI, 201
SAT-based Explicit LTLf Satisfiability Checking
We present here a SAT-based framework for LTLf (Linear Temporal Logic on
Finite Traces) satisfiability checking. We use propositional SAT-solving
techniques to construct a transition system for the input LTLf formula;
satisfiability checking is then reduced to a path-search problem over this
transition system. Furthermore, we introduce CDLSC (Conflict-Driven LTLf
Satisfiability Checking), a novel algorithm that leverages information produced
by propositional SAT solvers from both satisfiability and unsatisfiability
results. Experimental evaluations show that CDLSC outperforms all other
existing approaches for LTLf satisfiability checking, by demonstrating an
approximate four-fold speedup compared to the second-best solver
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