Density Condensation of Boolean Formulas
نویسندگان
چکیده
The following problem is considered: given a Boolean formula f, generate another formula g such that: (i) If f is unsatisfiable then g is also unsatisfiable. (ii) If f is satisfiable then g is also satisfiable and furthermore g is “easier” than f. For the measure of this easiness, we use the density of a formula f which is defined as (the number of satisfying assignments)/2n, where n is the number of Boolean variables of f. In this paper, we mainly consider the case that the input formula f is given as a 3-CNF formula and the output formula g may be any formula using Boolean AND, OR and negation. Two different approaches to this problem are presented: one is to obtain g by reducing the number of variables and the other by increasing the number of variables, both of which are based on existing SAT algorithms. Our performance evaluation shows that, a little surprisingly, better SAT algorithms do not always give us better density-condensation algorithms. © 2006 Elsevier B.V. All rights reserved.
منابع مشابه
Computing the Density of States of Boolean Formulas
In this paper we consider the problem of computing the density of states of a Boolean formula in CNF, a generalization of both MAX-SAT and model counting. Given a Boolean formula F , its density of states counts the number of configurations that violate exactly E clauses, for all values of E. We propose a novel Markov Chain Monte Carlo algorithm based on flat histogram methods that, despite the...
متن کاملExpressiveness and Complexity of Subclasses of Quantified Boolean Formulas
We give a brief overview of expressiveness and complexity results for a hierarchy of subclasses of quantified Boolean formulas with close connections to Boolean circuits and minimal unsatisfiability.
متن کاملBose-Einstein Condensation in Satisfiability Problems
This paper is concerned with the complex behavior arising in satisfiability problems. We present a new statistical physics-based characterization of the satisfiability problem. Specifically, we design an algorithm that is able to produce graphs starting from a k–SAT instance, in order to analyze them and show whether a Bose-Einstein condensation occurs. We observe that, analogously to complex n...
متن کاملDiscrete Optimization Bose–Einstein condensation in satisfiability problems
0377-2217/$ see front matter 2012 Elsevier B.V. A http://dx.doi.org/10.1016/j.ejor.2012.11.039 ⇑ Corresponding author. Tel.: +39 095 738 3048; fa E-mail addresses: [email protected] ( unict.it (A. Occhipinti), [email protected] (G. S unict.it (G. Nicosia). This paper is concerned with the complex behavior arising in satisfiability problems. We present a new statistical physics-ba...
متن کاملA Verified Decision Procedure for Pseudo-Boolean Formulas
Pseudo-Boolean formulas consist of constraints of the form ∑i=1 wi · xi k, where xi are propositional literals, wi ∈ Z, k ∈ Z, and arise in planning, scheduling and optimization problems. We describe an efficient and easily verifiable decision procedure for pseudo-Boolean formulas, that is based on encoding PB formulas into the propositional satisfiability problem with the cutting-edge sequenti...
متن کامل