Related papers: Recursive Backdoors for SAT
A backdoor set is a set of variables of a propositional formula such that fixing the truth values of the variables in the backdoor set moves the formula into some polynomial-time decidable class. If we know a small backdoor set we can…
Backdoor sets, a notion introduced by Williams et al. in 2003, are certain sets of key variables of a CNF formula F that make it easy to solve the formula; by assigning truth values to the variables in a backdoor set, the formula gets…
Propositional satisfiability (SAT) is at the nucleus of state-of-the-art approaches to a variety of computationally hard problems, one of which is cryptanalysis. Moreover, a number of practical applications of SAT can only be tackled…
There are various approaches to exploiting "hidden structure" in instances of hard combinatorial problems to allow faster algorithms than for general unstructured or random instances. For SAT and its counting version #SAT, hidden structure…
In the context of CSPs, a strong backdoor is a subset of variables such that every complete assignment yields a residual instance guaranteed to have a specified property. If the property allows efficient solving, then a small strong…
In this paper, we introduce a notion of backdoors to Reiter's propositional default logic and study structural properties of it. Also we consider the problems of backdoor detection (parameterised by the solution size) as well as backdoor…
For several decades, much effort has been put into identifying classes of CNF formulas whose satisfiability can be decided in polynomial time. Classic results are the linear-time tractability of Horn formulas (Aspvall, Plass, and Tarjan,…
Abductive reasoning (or Abduction, for short) is among the most fundamental AI reasoning methods, with a broad range of applications, including fault diagnosis, belief revision, and automated planning. Unfortunately, Abduction is of high…
Answer Set Programming (ASP) is an increasingly popular framework for declarative programming that admits the description of problems by means of rules and constraints that form a disjunctive logic program. In particular, many AI problems…
We show that CSP is fixed-parameter tractable when parameterized by the treewidth of a backdoor into any tractable CSP problem over a finite constraint language. This result combines the two prominent approaches for achieving tractability…
In this paper we extend the classical notion of strong and weak backdoor sets for SAT and CSP by allowing that different instantiations of the backdoor variables result in instances that belong to different base classes; the union of the…
Knuth (1990) introduced the class of nested formulas and showed that their satisfiability can be decided in polynomial time. We show that, parameterized by the size of a smallest strong backdoor set to the target class of nested formulas,…
Over the last two decades, propositional satisfiability (SAT) has become one of the most successful and widely applied techniques for the solution of NP-complete problems. The aim of this paper is to investigate theoretically how Sat can be…
We extend the notion of a strong backdoor from the CSP setting to the Valued CSP setting (VCSP, for short). This provides a means for augmenting a class of tractable VCSP instances to instances that are outside the class but of small…
In the present paper we introduce the notion of strong backdoors into the field of temporal logic for the CNF-fragment of linear temporal logic introduced by Fisher. We study the parameterised complexity of the satisfiability problem…
Backdoors of answer-set programs are sets of atoms that represent clever reasoning shortcuts through the search space. Assignments to backdoor atoms reduce the given program to several programs that belong to a tractable target class.…
A backdoor in a finite-domain CSP instance is a set of variables where each possible instantiation moves the instance into a polynomial-time solvable class. Backdoors have found many applications in artificial intelligence and elsewhere,…
Over the years complexity theorists have proposed many structural parameters to explain the surprising efficiency of conflict-driven clause-learning (CDCL) SAT solvers on a wide variety of large industrial Boolean instances. While some of…
In spite of the close connection between the evaluation of quantified Boolean formulas (QBF) and propositional satisfiability (SAT), tools and techniques which exploit structural properties of SAT instances are known to fail for QBF. This…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…