Search results for "satisfiability"
showing 10 items of 34 documents
Efficient CNF Encoding of Boolean Cardinality Constraints
2003
In this paper, we address the encoding into CNF clauses of Boolean cardinality constraints that arise in many practical applications. The proposed encoding is efficient with respect to unit propagation, which is implemented in almost all complete CNF satisfiability solvers. We prove the practical efficiency of this encoding on some problems arising in discrete tomography that involve many cardinality constraints. This encoding is also used together with a trivial variable elimination in order to re-encode parity learning benchmarks so that a simple Davis and Putnam procedure can solve them.
The fluted fragment with transitive relations
2022
Abstract The fluted fragment is a fragment of first-order logic (without equality) in which, roughly speaking, the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that this fragment has the finite model property. We consider extensions of the fluted fragment with various numbers of transitive relations, as well as the equality predicate. In the presence of one transitive relation (together with equality), the finite model property is lost; nevertheless, we show that the satisfiability and finite satisfiability problems for this extension remain decidable. We also show that the corresponding problems in the…
Two-variable First-Order Logic with Counting in Forests
2018
We consider an extension of two-variable, first-order logic with counting quantifiers and arbitrarily many unary and binary predicates, in which one distinguished predicate is interpreted as the mother-daughter relation in an unranked forest. We show that both the finite satisfiability and the general satisfiability problems for the extended logic are decidable in NExpTime. We also show that the decision procedure for finite satisfiability can be extended to the logic where two distinguished predicates are interpreted as the mother-daughter relations in two independent forests.
On the satisfiability problem for fragments of two-variable logic with one transitive relation
2019
Abstract We study the satisfiability problem for two-variable first-order logic over structures with one transitive relation. We show that the problem is decidable in 2-NExpTime for the fragment consisting of formulas where existential quantifiers are guarded by transitive atoms. As this fragment enjoys neither the finite model property nor the tree model property, to show decidability we introduce a novel model construction technique based on the infinite Ramsey theorem. We also point out why the technique is not sufficient to obtain decidability for the full two-variable logic with one transitive relation; hence, contrary to our previous claim, [FO$^2$ with one transitive relation is deci…
The complexity of finite model reasoning in description logics
2005
AbstractWe analyse the complexity of finite model reasoning in the description logic ALCQI, i.e., ALC augmented with qualifying number restrictions, inverse roles, and general TBoxes. It turns out that all relevant reasoning tasks such as concept satisfiability and ABox consistency are ExpTime-complete, regardless of whether the numbers in number restrictions are coded unarily or binarily. Thus, finite model reasoning with ALCQI is not harder than standard reasoning with ALCQI.
Classical and Quantum Annealing in the Median of Three Satisfiability
2011
We determine the classical and quantum complexities of a specific ensemble of three-satisfiability problems with a unique satisfying assignment for up to N = 100 and 80 variables, respectively. In the classical limit, we employ generalized ensemble techniques and measure the time that a Markovian Monte Carlo process spends in searching classical ground states. In the quantum limit, we determine the maximum finite correlation length along a quantum adiabatic trajectory determined by the linear sweep of the adiabatic control parameter in the Hamiltonian composed of the problem Hamiltonian and the constant transverse field Hamiltonian. In the median of our ensemble, both complexities diverge e…
Combining finite learning automata with GSAT for the satisfiability problem
2010
A large number of problems that occur in knowledge-representation, learning, very large scale integration technology (VLSI-design), and other areas of artificial intelligence, are essentially satisfiability problems. The satisfiability problem refers to the task of finding a satisfying assignment that makes a Boolean expression evaluate to True. The growing need for more efficient and scalable algorithms has led to the development of a large number of SAT solvers. This paper reports the first approach that combines finite learning automata with the greedy satisfiability algorithm (GSAT). In brief, we introduce a new algorithm that integrates finite learning automata and traditional GSAT use…
Topological Logics with Connectedness over Euclidean Spaces
2013
We consider the quantifier-free languages, Bc and Bc °, obtained by augmenting the signature of Boolean algebras with a unary predicate representing, respectively, the property of being connected, and the property of having a connected interior. These languages are interpreted over the regular closed sets of R n ( n ≥ 2) and, additionally, over the regular closed semilinear sets of R n . The resulting logics are examples of formalisms that have recently been proposed in the Artificial Intelligence literature under the rubric Qualitative Spatial Reasoning. We prove that the satisfiability problem for Bc is undecidable over the regular closed semilinear sets in all dimensions greater than 1,…
Two-variable logics with counting and semantic constraints
2018
In this article we discuss fragments and extensions of two-variable logics motivated by practical applications. We outline the decidability frontier, describing some of the techniques developed for deciding satisfiability and finite satisfiability, as well as characterizing their complexity.
Some Computational Aspects of DISTANCE-SAT
2007
In many AI fields, one must face the problem of finding a solution that is as close as possible to a given configuration. This paper addresses this problem in a propositional framework. We introduce the decision problem distance-sat, which consists in determining whether a propositional formula admits a model that disagrees with a given partial interpretation on at most d variables. The complexity of distance-sat and of several restrictions of it are identified. Two algorithms based on the well-known Davis/Logemann/Loveland search procedure for the satisfiability problem sat are presented so as to solve distance-sat for CNF formulas. Their computational behaviors are compared with the ones …