This paper discusses a model of constraint satisfaction problems known as uniquely extendible constraint satisfaction problems. This model includes and generalizes XOR-SAT, and the model includes an NP-complete problem that appears to share many of the threshold characteristics of random SAT. In this paper we find an exact threshold in the behavior of two versions of DPLL on random instances of...

The past decade has seen clause learning as the most successful algorithm for SAT instances arising from real-world applications. This practical success is accompanied by theoretical results showing clause learning as equivalent in power to resolution. There exist, however, problems that are intractable for resolution, for which clause-learning solvers are hence doomed. In this paper, we presen...

In spoken language, parentheticals are marked by a special intonation: -clear breaks before and after; -spoken faster or slower than the main clause; -lower pitch of the voice. The intonation contour of the main clause is continued after the end of the parenthetical. Intuitively it is obvious, what parentheticals are: Expressions, ranging from single words to complex clauses, are built in into ...

Lazy clause generation is a powerful hybrid approach to combinatorial optimization that combines features from SAT solving and finite domain (FD) propagation. In lazy clause generation finite domain propagators are considered as clause generators that create a SAT description of their behaviour for a SAT solver. The ability of the SAT solver to explain and record failure and perform conflict di...

Input Distance ( ) is introduced as a metric for propositional resolution derivations. If F = Ci is a formula and D is a clause, then (D;F) is de ned as minijD Cij. The for a derivation is the maximum of any clause in the derivation. Input Distance provides a re nement of the clause-width metric analyzed by Ben-Sasson and Wigderson (JACM 2001) in that it applies to families whose clause width g...

The technique of watching two literals per clause to determine when a clause becomes a unit clause was introduced recently in the Chaff satisfiability program. That program does not perform either equivalent-literal detection or binary-clause detection. We describe a generalization of the technique that handles the tracking necessary to support equivalent-literal detection and binary-clause det...

ILP systems which use some form of Inverse Entailment (IE) are based on clause refinement through a hypotheses space bounded by a most specific clause. In this paper we give a new analysis of refinement operators in this setting. In particular, Progol’s refinement operator is revisited and discussed. It is known that Progol’s refinement operator is incomplete with respect to the general subsump...

consisting of a conjunction of clauses, where a clause is a disjunction of literals; a literal is either a variable v (a positive literal) or the negation of a variable ¬v (a negative literal). We are to decide if there is an assignment to the variables satisfying the formula, that is, an assignment under which every clause contains at least one true literal. The example formula is satisfied by...

Existing proposals for implementing the run-time suspension test for GHC concentrate upon suspending unifications in the bodies of clauses being used to evaluate guard literals. However, by making simple alterations to the guard and adding special primitives to it to localise the requirement to suspend to a primitive in the guard, unifications in the bodies of clauses may proceed without being ...

consisting of a conjunction of clauses, where a clause is a disjunction of literals; a literal is either a variable v (a positive literal) or the negation of a variable ¬v (a negative literal). We are to decide if there is an assignment to the variables satisfying the formula, that is, an assignment under which every clause contains at least one true literal. The example formula is satisfied by...