Related papers: Empirical Challenge for NC Theory
A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set B of Boolean functions. We consider the problem of determining whether two given constraint…
Partly on the basis of heuristic arguments from physics it has been suggested that the performance of certain types of algorithms on random $k$-SAT formulas is linked to phase transitions that affect the geometry of the set of satisfying…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
Many procedures for SAT and SAT-related problems -- in particular for those requiring the complete enumeration of satisfying truth assignments -- rely their efficiency on the detection of partial assignments satisfying an input formula. In…
Characteristic models are an alternative, model based, representation for Horn expressions. It has been shown that these two representations are incomparable and each has its advantages over the other. It is therefore natural to ask what is…
We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn…
In the article \The State of SAT", the authors asked whether a procedure dramatically different from DPLL can be found for handling unsatisfiable instances. This study proposes a new linear programming approach to address this issue…
The satisfiability problem is known to be $\mathbf{NP}$-complete in general and for many restricted cases. One way to restrict instances of $k$-SAT is to limit the number of times a variable can be occurred. It was shown that for an…
We study the Boolean Satisfiability problem (SAT) in the framework of diversity, where one asks for multiple solutions that are mutually far apart (i.e., sufficiently dissimilar from each other) for a suitable notion of…
The Boolean Satisfiability problem (SAT) is important on artificial intelligence community and the impact of its solving on complex problems. Recently, great breakthroughs have been made respectively on stochastic local search (SLS)…
The use of temporal logics has long been recognised as a fundamental approach to the formal specification and verification of reactive systems. In this paper, we take on the problem of automatically verifying a temporal property, given by a…
We present a novel application of the Kramers-Wannier duality on one of the most important problems of computer science, the Boolean satisfiability problem (SAT). More specifically, we focus on sharp-SAT or equivalently #SAT - the problem…
Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…
Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…
This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…
To test incomplete search algorithms for constraint satisfaction problems such as 3-SAT, we need a source of hard, but satisfiable, benchmark instances. A simple way to do this is to choose a random truth assignment A, and then choose…
Horn functions form a subclass of Boolean functions and appear in many different areas of computer science and mathematics as a general tool to describe implications and dependencies. Finding minimum sized representations for such functions…
The problem of estimating the proportion of satisfiable instances of a given CSP (constraint satisfaction problem) can be tackled through weighting. It consists in putting onto each solution a non-negative real value based on its…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
Boolean Satisfiability (SAT) problems are expressed as mathematical formulas. This paper presents a matrix representation for these SAT problems. It shows how to use this matrix representation to get the full set of valid satisfying…