159 research outputs found
An Information-Based Neural Approach to Constraint Satisfaction
A novel artificial neural network approach to constraint satisfaction
problems is presented. Based on information-theoretical considerations, it
differs from a conventional mean-field approach in the form of the resulting
free energy. The method, implemented as an annealing algorithm, is numerically
explored on a testbed of K-SAT problems. The performance shows a dramatic
improvement to that of a conventional mean-field approach, and is comparable to
that of a state-of-the-art dedicated heuristic (Gsat+Walk). The real strength
of the method, however, lies in its generality -- with minor modifications it
is applicable to arbitrary types of discrete constraint satisfaction problems.Comment: 13 pages, 3 figures,(to appear in Neural Computation
The Phase Diagram of 1-in-3 Satisfiability Problem
We study the typical case properties of the 1-in-3 satisfiability problem,
the boolean satisfaction problem where a clause is satisfied by exactly one
literal, in an enlarged random ensemble parametrized by average connectivity
and probability of negation of a variable in a clause. Random 1-in-3
Satisfiability and Exact 3-Cover are special cases of this ensemble. We
interpolate between these cases from a region where satisfiability can be
typically decided for all connectivities in polynomial time to a region where
deciding satisfiability is hard, in some interval of connectivities. We derive
several rigorous results in the first region, and develop the
one-step--replica-symmetry-breaking cavity analysis in the second one. We
discuss the prediction for the transition between the almost surely satisfiable
and the almost surely unsatisfiable phase, and other structural properties of
the phase diagram, in light of cavity method results.Comment: 30 pages, 12 figure
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