Gilles Dequen

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 inconsistent clause-subsets for Max-SAT solving

Recent research has focused on using the power of look-ahead to speed up the resolution of the Max-SAT problem. Indeed, look-ahead techniques such as Unit Propagation (UP) allow to find conflicts and to quickly reach the upper bound in a Branch-and-Bound algorithm, reducing the search-space of the resolution. In previous works, the Max-SAT solvers maxsatz9 and maxsatz14 use unit propagation to compute, at each node of the branch and bound search-tree, disjoint inconsistent subsets of clauses in the current subformula to estimate the minimum number of clauses that cannot be satisfied by any assignment extended from the current node. The same subsets may still be present in the subtrees, that is why we present in this paper a new method to memorize them and then spare their recomputation time. Furthermore, we propose a heuristic so that the memorized subsets of clauses induce an ordering among unit clauses to detect more inconsistent subsets of clauses. We show that this new approach improves maxsatz9 and maxsatz14 and suggest that the approach can also be used to improve other state-of-the-art Max-SAT solvers.

Using Boolean Constraint Propagation for sub-clauses deduction

The Boolean Constraint Propagation (BCP) is a well-known helpful technique implemented in most state-of-the-art efficient satisfiability solvers. We propose in this paper a new use of the BCP to deduce sub-clauses from the associated implication graph. Our aim is to reduce the length of clauses thanks to the subsumption rule. We show how such extension can be grafted to modern SAT solvers and we provide some experimental results of the sub-clauses deduction as a pretreatment process. This work is supported by the Region Picardie under HTSC project.

Stochastic Local Search for Omnidirectional Catadioptric Stereovision Design

This paper deals with a compact catadioptric omnidirectional stereovision system based on a single camera and multi-mirrors (at least two mirrors). Many configurations were empirically designed in previous works with the aim to obtain a good 3D reconstruction accuracy. In this paper, we propose to use optimization techniques for omnidirectional catadioptric stereovision design, by using a stochastic local search method in order to find a good sensor (number, relative positions and sizes of mirrors). We explain principles of our approach and provide automatically designed sensors with a number of mirrors from two to nine. We finally simulate the 3D-reconstruction of a real environment modeled under a ray-tracing software with some of these sensors.

An Efficient Approach to Solving Random k-sat Problems

Proving that a propositional formula is contradictory or unsatisfiable is a fundamental task in automated reasoning. This task is coNP-complete. Efficient algorithms are therefore needed when formulae are hard to solve. Random

Encoding Hash Functions as a SAT Problem

k-

Toward Easy Parallel SAT Solving

sat formulae provide a test-bed for algorithms because experiments that have become widely popular show clearly that these formulae are consistently difficult for any known algorithm. Moreover, the experiments show a critical value of the ratio of the number of clauses to the number of variables around which the formulae are the hardest on average. This critical value also corresponds to a ‘phase transition’ from solvability to unsolvability. The question of whether the formulae located around or above this critical value can efficiently be proved unsatisfiable on average (or even for a.e. formula) remains up to now one of the most challenging questions bearing on the design of new and more efficient algorithms. New insights into this question could indirectly benefit the solving of formulae coming from real-world problems, through a better understanding of some of the causes of problem hardness. In this paper we present a solving heuristic that we have developed, devoted essentially to proving the unsatisfiability of random

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

k-

On multi-threaded satisfiability solving with OpenMP

sat formulae and inspired by recent work in statistical physics. Results of experiments with this heuristic and its evaluation in two recent sat competitions have shown a substantial jump in the efficiency of solving hard, unsatisfiable random

High Performance CGM-based Parallel Algorithms for the Optimal Binary Search Tree Problem

k-