0000000000064522
AUTHOR
Olivier Bailleux
Subsumption-driven clause learning with DPLL+restarts
We propose to use a DPLL+restart to solve SAT instances by successive simplifications based on the production of clauses that subsume the initial clauses. We show that this approach allows the refutation of pebbling formulae in polynomial time and linear space, as effectively as with a CDCL solver.
Counting by Statistics on Search Trees: Application to Constraint Satisfaction Problems
In 1975, Knuth proposed a simple statistical method for investigating search trees. We use this technique for estimating the number of solutions of constraint satisfaction problem CSP and boolean satisfiability problem SAT instances. We show that, depending on domain reductions, tree-based estimates have a lower variance than estimates based on uniform sampling from the search space. Nevertheless, because the variance remains extremely high in the general case, a confidence interval cannot be derived, but a lower bound of the number of solutions. These results are confirmed by many experiments.
A Translation of Pseudo Boolean Constraints to SAT
Research note; This paper introduces a new CNF encoding of pseudo-Boolean constraints, which allows unit propagation to maintain generalized arc consistency. In the worst case, the size of the produced formula can be exponentially related to the size of the input constraint, but some important classes of pseudo-Boolean constraints, including Boolean cardinality constraints, are encoded in polynomial time and size. The proposed encoding was integrated in a solver based on the zCha SAT solver and submitted to the PB05 evaluation. The results provide new perspectives in the field of full CNF approach of pseudo-Boolean constraints solving.
New Encodings of Pseudo-Boolean Constraints into CNF
International audience; This paper answers affirmatively the open question of the existence of a polynomial size CNF encoding of pseudo-Boolean (PB) constraints such that generalized arc consistency (GAC) is maintained through unit propagation (UP). All previous encodings of PB constraints either did not allow UP to maintain GAC, or were of exponential size in the worst case. This paper presents an encoding that realizes both of the desired properties. From a theoretical point of view, this narrows the gap between the expressive power of clauses and the one of pseudo-Boolean constraints.
Unit contradiction versus unit propagation
Some aspects of the result of applying unit resolution on a CNF formula can be formalized as functions with domain a set of partial truth assignments. We are interested in two ways for computing such functions, depending on whether the result is the production of the empty clause or the assignment of a variable with a given truth value. We show that these two models can compute the same functions with formulae of polynomially related sizes, and we explain how this result is related to the CNF encoding of Boolean constraints.
Attempts to produce minimal Resolution refutations
We address the challenge of searching minimal refutations proofs of inconsistent CNF formulae using the Resolution rule. We propose two algorithms which can only afford formulae of at most 5 variables with a desktop computer. A faster but incomplete algorithm is used to produce "hard" 5 variables 3CNF formulae though a stochastic greedy search. It allowed us to find formulae that can be refuted by producing clauses of at most 3 literals, but whose all minimal refutations contain at least one clause of 4 literals.
Full CNF Encoding: The Counting Constraints Case
Many problems are naturally expressed using CNF clauses and boolean cardinality constraints. It is generally believed that solving such problems through pure CNF encoding is inefficient, so many authors has proposed specialized algorithms : the pseudo-boolean solvers. In this paper we show that an appropriate pure CNF encoding can be competitive with these specialized methods. In conjunction with our encoding, we propose a slight modification of the DLL procedure that allows any DLL-based SAT solver to solve boolean cardinality optimization problems. We show experimentally that our encoding allows zchaff to be competitive with pseudo-boolean solvers on some decision and optimization problem…
Measuring the Spatial Dispersion of Evolutionary Search Processes: Application to Walksat
In this paper, we propose a simple and efficient method for measuring the spatial dispersion of a set of points in a metric space. This method allows the quantifying of the population diversity in genetic algorithms. It can also be used to measure the spatial dispersion of any local search process during a specified time interval. We then use this method to study the way Walksat explores its search space, showing that the search for a solution often includes several stages of intensification and diversification.
Efficient CNF Encoding of Boolean Cardinality Constraints
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.
Research of Complex Forms in Cellular Automata by Evolutionary Algorithms
This paper presents an evolutionary approach for the search for new complex cellular automata. Two evolutionary algorithms are used: the first one discovers rules supporting gliders and periodic patterns, and the second one discovers glider guns in cellular automata. An automaton allowing us to simulate AND and NOT gates is discovered. The results are a step toward the general simulation of Boolean circuits by this automaton and show that the evolutionary approach is a promising technic for searching for cellular automata that support universal computation.
DPLL with restarts linearly simulates CDCL
If we give DPLL the ability to make restarts and to learn clauses representing the explored search space, it can linearly simulate CDCL solvers.
Research of a Cellular Automaton Simulating Logic Gates by Evolutionary Algorithms
This paper presents a method of using genetic programming to seek new cellular automata that perform computational tasks. Two genetic algorithms are used : the first one discovers a rule supporting gliders and the second one modifies this rule in such a way that some components appear allowing it to simulate logic gates. The results show that the genetic programming is a promising tool for the search of cellular automata with specific behaviors, and thus can prove to be decisive for discovering new automata supporting universal computation.
A New Universal Cellular Automaton Discovered by Evolutionary Algorithms
In Twenty Problems in the Theory of Cellular Automata, Stephen Wolfram asks “how common computational universality and undecidability [are] in cellular automata.” This papers provides elements of answer, as it describes how another universal cellular automaton than the Game of Life (Life) was sought and found using evolutionary algorithms. This paper includes a demonstration that consists in showing that the presented R automaton can both implement any logic circuit (logic universality) and a simulation of Life (universality in the Turing sense).
Some Computational Aspects of DISTANCE-SAT
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 …