Olivier Dubois

kcnfs : An Efficient Solver for Random k -SAT Formulae

In this paper we generalize a heuristic that we have introduced previously for solving efficiently random 3-SAT formulae. Our heuristic is based on the notion of backbone, searching variables belonging to local backbones of a formula. This heuristic was limited to 3-SAT formulae. In this paper we generalize this heuristic by introducing a sub-heuristic called a re-normalization heuristic in order to handle formulae with various clause lengths and particularly hard random k-sat formulae with k ≥ 3 . We implemented this new general heuristic in our previous program cnfs, a classical dpll algorithm, renamed kcnfs. We give experimental results which show that kcnfs outperforms by far the best current complete solvers on any random k-SAT formula for k ≥ 3.

On the r,s satisfiability problem and a conjecture of Tovey

Abstract We denote by r , s -SAT the class of instances of the satisfiability problem in which every clause contains exactly r variables, and every variable has a most s occurrences. We show that the satisfiability of a class r 0 , s 0 -SAT implies the satisfiability of classes r , s -SAT, for certain well-defined higher value of r and s . We disprove a related conjecture of Tovey.

Approximating the Satisfiability Threshold for Random k -XOR-formulas

In this paper we study random linear systems with

Secreted surfactant protein A from fetal membranes induces stress fibers in cultured human myometrial cells

k > 3

Differential Expression of the Enzymatic System Controlling Synthesis, Metabolism, and Transport of PGF2 Alpha in Human Fetal Membranes

variables per equation over the finite field GF(2), or equivalently k-XOR-CNF formulas. In a previous paper Creignou and Daude proved that there exists a phase transition exhibiting a sharp threshold, for the consistency (satisfiability) of such systems (formulas). The control parameter for this transition is the ratio of the number of equations to the number of variables, and the scale for which the transition occurs remains somewhat elusive. In this paper we establish, for any

An Efficient Approach to Solving Random k-sat Problems

k > 3

Reconstructing (h,v)-convex 2-dimensional patterns of objects from approximate horizontal and vertical projections

, non-trivial lower and upper estimates of the value of the control ratio for which the phase transition occurs. For

The 3-XORSAT threshold

k=3

The Non-existence of (3, 1, 2)-Conjugate Orthogonal Idempotent Latin Square of Order 10

we get 0.89 and 0.93, respectively. Moreover, we give experimental results for

Additive Decompositions, Random Allocations, and Threshold Phenomena

k=3