相关论文: Islands for SAT

We propose to use local search algorithms to produce SAT instances which are harder to solve than randomly generated k-CNF formulae. The first results, obtained with rudimentary search algorithms, show that the approach deserves further…

A generalized 1-in-3SAT problem is defined and found to be in complexity class P when restricted to a certain subset of CNF expressions. In particular, 1-in-kSAT with no restrictions on the number of literals per clause can be decided in…

We study local-search satisfiability solvers for propositional logic extended with cardinality atoms, that is, expressions that provide explicit ways to model constraints on cardinalities of sets. Adding cardinality atoms to the language of…

The aim of this short note is mainly pedagogical. It summarizes some knowledge about Boolean satisfiability (SAT) and the P=NP? problem in an elementary mathematical language. A convenient scheme to visualize and manipulate CNF formulae is…

We explore the idea of using finite automata to implement new constraints for local search (this is already a successful technique in constraint-based global search). We show how it is possible to maintain incrementally the violations of a…

Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information…

Applying pre- and inprocessing techniques to simplify CNF formulas both before and during search can considerably improve the performance of modern SAT solvers. These algorithms mostly aim at reducing the number of clauses, literals, and…

The Constraint Satisfaction Problem (CSP) is a central and generic computational problem which provides a common framework for many theoretical and practical applications. A central line of research is concerned with the identification of…

Local search algorithms use the neighborhood relations among search states and often perform well for a variety of NP-hard combinatorial search problems. This paper shows how quantum computers can also use these neighborhood relations. An…

Finding exact circuit size is a notorious optimization problem in practice. Whereas modern computers and algorithmic techniques allow to find a circuit of size seven in blink of an eye, it may take more than a week to search for a circuit…

This paper introduces the notion of Constrained Locating Arrays (CLAs), mathematical objects which can be used for fault localization in software testing. CLAs extend ordinary locating arrays to make them applicable to testing of systems…

Boolean Satisfiability Problem (SAT) is one of the core problems in computer science. As one of the fundamental NP-complete problems, it can be used - by known reductions - to represent instances of variety of hard decision problems.…

The Local Search algorithm (or Hill Climbing, or Iterative Improvement) is one of the simplest heuristics to solve the Satisfiability and Max-Satisfiability problems. It is a part of many satisfiability and max-satisfiability solvers, where…

We present a method for the enumeration of restricted words over a finite alphabet. Restrictions are described through the inclusion or exclusion of suitable building blocks used to construct the words by concatenation. Our approach, which…

Autarkies for SAT can be used for theoretical studies, pre-processing and inprocessing. They generalise satisfying assignments by allowing to leave some clauses "untouched" (no variable assigned). We introduce the natural generalisation to…

Islands are combinatorial objects that can be intuitively defined on a board consisting of a finite number of cells. Based on the neighbor relation of the cells, it is a fundamental property that two islands are either containing or…

Earlier we introduced the notion of a stable set of points (SSP). We proved that a CNF formula is unsatisfiable iff there is a set of points (i.e. complete assignments) that is stable with respect to this formula. Experiments showed that…

We propose an algorithm of generating hard instances for the Satisfying Assignment Search Problem (in short, SAT). The algorithm transforms instances of the integer factorization problem into SAT instances efficiently by using the Chinese…

A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…

The Local Lemma is a fundamental tool of probabilistic combinatorics and theoretical computer science, yet there are hardly any natural problems known where it provides an asymptotically tight answer. The main theme of our paper is to…