5,001 research outputs found
Generalizing Boolean Satisfiability I: Background and Survey of Existing Work
This is the first of three planned papers describing ZAP, a satisfiability
engine that substantially generalizes existing tools while retaining the
performance characteristics of modern high-performance solvers. The fundamental
idea underlying ZAP is that many problems passed to such engines contain rich
internal structure that is obscured by the Boolean representation used; our
goal is to define a representation in which this structure is apparent and can
easily be exploited to improve computational performance. This paper is a
survey of the work underlying ZAP, and discusses previous attempts to improve
the performance of the Davis-Putnam-Logemann-Loveland algorithm by exploiting
the structure of the problem being solved. We examine existing ideas including
extensions of the Boolean language to allow cardinality constraints,
pseudo-Boolean representations, symmetry, and a limited form of quantification.
While this paper is intended as a survey, our research results are contained in
the two subsequent articles, with the theoretical structure of ZAP described in
the second paper in this series, and ZAP's implementation described in the
third
Dynamic Backtracking
Because of their occasional need to return to shallow points in a search
tree, existing backtracking methods can sometimes erase meaningful progress
toward solving a search problem. In this paper, we present a method by which
backtrack points can be moved deeper in the search space, thereby avoiding this
difficulty. The technique developed is a variant of dependency-directed
backtracking that uses only polynomial space while still providing useful
control information and retaining the completeness guarantees provided by
earlier approaches.Comment: See http://www.jair.org/ for an online appendix and other files
accompanying this articl
GIB: Imperfect Information in a Computationally Challenging Game
This paper investigates the problems arising in the construction of a program
to play the game of contract bridge. These problems include both the difficulty
of solving the game's perfect information variant, and techniques needed to
address the fact that bridge is not, in fact, a perfect information game. GIB,
the program being described, involves five separate technical advances:
partition search, the practical application of Monte Carlo techniques to
realistic problems, a focus on achievable sets to solve problems inherent in
the Monte Carlo approach, an extension of alpha-beta pruning from total orders
to arbitrary distributive lattices, and the use of squeaky wheel optimization
to find approximately optimal solutions to cardplay problems. GIB is currently
believed to be of approximately expert caliber, and is currently the strongest
computer bridge program in the world
Generalizing Boolean Satisfiability II: Theory
This is the second of three planned papers describing ZAP, a satisfiability
engine that substantially generalizes existing tools while retaining the
performance characteristics of modern high performance solvers. The fundamental
idea underlying ZAP is that many problems passed to such engines contain rich
internal structure that is obscured by the Boolean representation used; our
goal is to define a representation in which this structure is apparent and can
easily be exploited to improve computational performance. This paper presents
the theoretical basis for the ideas underlying ZAP, arguing that existing ideas
in this area exploit a single, recurring structure in that multiple database
axioms can be obtained by operating on a single axiom using a subgroup of the
group of permutations on the literals in the problem. We argue that the group
structure precisely captures the general structure at which earlier approaches
hinted, and give numerous examples of its use. We go on to extend the
Davis-Putnam-Logemann-Loveland inference procedure to this broader setting, and
show that earlier computational improvements are either subsumed or left intact
by the new method. The third paper in this series discusses ZAPs implementation
and presents experimental performance results
Generalizing Boolean Satisfiability III: Implementation
This is the third of three papers describing ZAP, a satisfiability engine
that substantially generalizes existing tools while retaining the performance
characteristics of modern high-performance solvers. The fundamental idea
underlying ZAP is that many problems passed to such engines contain rich
internal structure that is obscured by the Boolean representation used; our
goal has been to define a representation in which this structure is apparent
and can be exploited to improve computational performance. The first paper
surveyed existing work that (knowingly or not) exploited problem structure to
improve the performance of satisfiability engines, and the second paper showed
that this structure could be understood in terms of groups of permutations
acting on individual clauses in any particular Boolean theory. We conclude the
series by discussing the techniques needed to implement our ideas, and by
reporting on their performance on a variety of problem instances
Layered XY-Models, Anyon Superconductors, and Spin-Liquids
The partition function of the double-layer model in the (dual) Villain
form is computed exactly in the limit of weak coupling between layers. Both
layers are found to be locked together through the
Berezinskii-Kosterlitz-Thouless transition, while they become decoupled well
inside the normal phase. These results are recovered in the general case of a
finite number of such layers. When re-interpreted in terms of the dual problems
of lattice anyon superconductivity and of spin-liquids, they also indicate that
the essential nature of the transition into the normal state found in two
dimensions persists in the case of a finite number of weakly coupled layers.Comment: 10 pgs, TeX, LA-UR-94-394
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