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

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

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 $XY$ 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

Superconducting properties of ultrathin Bi2Sr2CaCu2O8+x single crystals

We use Ar-ion milling to thin Bi2212 single crystals down to a few nanometers or one-to-two (CuO2)2 layers. With decreasing the thickness, superconducting transition temperature gradually decreases to zero and the in-plane resistivity increases to large values indicating the existence of a superconductor-insulator transition in ultrathin Bi2212 single crystals.Comment: 17 pages, 6 figures, to appear in J. Appl. Phys. 98(3) 200

The use of nerve and muscle biopsy in the diagnosis of vasculitis: a 5 year retrospective study

INTRODUCTION: Peripheral nerve vasculitis is an important condition which can be diagnostically challenging and is one of the principal current indications for nerve and muscle biopsy. Previous studies have suggested that combined nerve and muscle biopsy (usually of the superficial peroneal nerve and peroneus brevis muscle) produces a higher diagnostic yield than nerve biopsy alone in the investigation of vasculitis. OBJECTIVE: To determine whether in our two centres combined nerve (usually the sural) and muscle (usually the vastus lateralis) biopsy improved diagnostic yield compared with nerve biopsy alone. METHODS: We interrogated our database of all nerve biopsies (usually of the sural nerve) performed at our institutions over 5 years and identified 53 cases of biopsy proven peripheral nerve vasculitis. Clinicopathological and neurophysiological data in these patients were reviewed. RESULTS: The most common clinical presentation was with a painful asymmetric axonal polyneuropathy or mononeuritis multiplex (66% of cases). Nerve biopsy demonstrated definite vasculitis in 36%, probable vasculitis in 62% and no vasculitis in 2% of cases. In 24 patients a muscle biopsy (usually the vastus lateralis) was also performed and vasculitis was demonstrated in 46% of these (in 13% showing definite and 33% probable vasculitis). There was only one patient in whom vasculitis was demonstrated in muscle but not in peripheral nerve. CONCLUSION: Combined nerve (usually sural) and vastus lateralis muscle biopsy did not significantly increase the diagnostic yield compared with nerve biopsy alone. A sensible approach to the diagnosis of peripheral nerve vasculitis is to choose a nerve to biopsy which is clinically affected and amenable to biopsy. If the sural nerve is chosen, the data suggest that it is not routinely worth doing a vastus lateralis biopsy at the same time, whereas if the superficial peroneal nerve is chosen, it seems appropriate to do a combined superficial peroneal nerve and peroneus brevis biopsy. It is still not known if both the sural and superficial peroneal nerves are involved clinically which one gives the higher yield if biopsied