The paper compares two popular strategies for solving propositional satisfiability, backtracking search and resolution, and analyzes the complexity of a directional resolution algorithm (DR) as a function of the "width" (w) of the problem's graph.

. Many AI problems can be conveniently encoded as discrete constraint satisfaction problems. It is often the case that not all solutions to a CSP are equally desirable --- in general, one is interested in a set of "preferred" solutions (for example, solutions that minimize some cost function) . Preferences can be encoded by incorporating "soft" constraints in the problem instance. We show how both hard and soft constraints can be handled by encoding problems as instances of weighted MAX-SAT (finding a model that maximizes the sum of the weights of the satisfied clauses that make up a problem instance). We generalize a local-search algorithm for satisfiability to handle weighted MAX-SAT. To demonstrate the effectiveness of our approach, we present experimental results on encodings of a set of well-studied network Steiner-tree problems. This approach turns out to be competitive with some of the best current specialized algorithms developed in operations research. 1. Introduction Traditi...

We report on the performance of an enhanced version of the "Davis-Putnam" (DP) proof procedure for propositional satisfiability (SAT) on large instances derived from realworld problems in planning, scheduling, and circuit diagnosis and synthesis. Our results show that incorporating CSP lookback techniques -- especially the relatively new technique of relevance-bounded learning -- renders easy many problems which otherwise are beyond DP's reach. Frequently they make DP, a systematic algorithm, perform as well or better than stochastic SAT algorithms such as GSAT or WSAT. We recommend that such techniques be included as options in implementations of DP, just as they are in systematic algorithms for the more general constraint satisfaction problem. Introduction While CNF propositional satisfiability (SAT) is a specific kind constraint satisfaction problem (CSP), until recently there has been little application of popular CSP look-back techniques in SAT algorithms. In previo...

Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default logic, as a source of large-scale problems needed for experimentation and as a source of intuitions needed for a systematic methodology of encoding problems as default theories we use here the domain of combinatorial problems. To experimentally study the performance of DeReS we developed a benchmarking system, the TheoryBase. The TheoryBase is designed to support experimental investigations of nonmonotonic reasoning systems based on the language of default logic or logic programming. It allows the user to create parameterized collections of default theories having similar properties and growing sizes and, consequently, to study the asymptotic performance of nonmonotonic systems under i...

In this paper, we describe a system, called TheoryBase, whose goal is to facilitate experimental studies of nonmonotonic reasoning systems. TheoryBase generates test default theories and logic programs. It has an identification system for generated theories, which allows us to reconstruct a logic program or a default theory from its identifier. Hence, exchanging test cases requires only exchanging identifiers. TheoryBase can generate a large variety of examples of default theories and logic programs. We believe that its universal adoption may significantly advance experimental studies of nonmonotonic reasoning systems.

We present a compiler that translates a problem specification into a propositional satisfiability test (SAT). Problems are specified in a logic-based language, called np-spec, which allows the definition of complex problems in a highly declarative way, and whose expressive power is such to capture exactly all problems which belong to the complexity class NP. The target SAT instance is solved using any of the various state-of-the-art solvers available from the community. The system obtained is an executable specification language for all NP problems which shows interesting computational properties. The performances of the system have been tested on a few classical problems, namely graph coloring, Hamiltonian cycle, and job-shop scheduling. c flSpringer-Verlag. To appear on the Proceedings of the European Symposium On Programming (ESOP 2001) Genova, Italy, April 2-6, 2001 Lecture Notes in Computer Science, Springer-Verlag, 2001. ftp://ftp.dis.uniroma1.it/pub/ai/papers/cado-scha-01.ps.gz 1

For many years, the intuitions underlying partial-order planning were largely taken for granted. Only in the past few years has there been renewed interest in the fundamental principles underlying this paradigm. In this paper, we present a rigorous comparative analysis of partial-order and total-order planning by focusing on two specific planners that can be directly compared. We show that there are some subtle assumptions that underly the wide-spread intuitions regarding the supposed efficiency of partial-order planning. For instance, the superiority of partial-order planning can depend critically upon the search strategy and the structure of the search space. Understanding the underlying assumptions is crucial for constructing efficient planners. 1. Introduction For many years, the superiority of partial-order planners over total-order planners has been tacitly assumed by the planning community. Originally, partial-order planning was introduced by Sacerdoti (1975) as a way to improv...

This paper presents an experimental investigation of the following questions: how does the average-case complexity of random 3-SAT, understood as a function of the order (number of variables) for xed density (ratio of number of clauses to order) instances, depend on the density? Is there a phase transition in which the complexity shifts from polynomial to exponential in the order? Is the transition dependent or independent of the solver? Our experiment design uses three complete SAT solvers embodying dierent algorithms: GRASP, CPLEX, and CUDD. We observe new phase transitions for all three solvers, where the median running time shifts from polynomial in the order to exponential. The location of the phase transition appears to be solver-dependent. While GRASP and CUDD shift from polynomial to exponential complexity at a density of about 3.8, CUDD exhibits this transition between densities of 0.1 and 0.5. This experimental result underscores the dependence between the solver and the complexity phase transition, and challenges the widely held belief that random 3-SAT exhibits a phase transition in computational complexity very close to the crossover point.

. We present a detailed experimental comparison of interleaved depth-first search and depth-bounded discrepancy search, two tree search procedures recently developed with the same goal: to reduce the cost of heuristic mistakes at the top of the tree. Our comparison uses an abstract heuristic model, and three different concrete problem classes: binary constraint satisfaction, quasigroup completion and number partitioning problems. Results indicate that both search strategies often reduce search. In addition, they show that their efficiency depends on a trade-off between the number of discrepancies (branch points against the heuristic) considered at the top of the tree, and the overhead of expanding branches from these discrepancies. If the number of discrepancies is large, the overhead can outweigh the benefits. 1 INTRODUCTION By definition, heuristics sometimes make mistakes. When searching a tree with depth-first search (Dfs), mistakes made at the top of the tree can be very costly ...

Much recent work has gone into adapting techniques that were originally developed for SAT solving to QBF solving. In particular, QBF solvers are often based on SAT solvers. Most competitive QBF solvers are search-based. In this work we explore an alternative approach to QBF solving, based on symbolic quantifier elimination. We extend some recent symbolic approaches for SAT solving to symbolic QBF solving, using various decision-diagram formalisms such as OBDDs and ZDDs. In both approaches, QBF formulas are solved by eliminating all their quantifiers. Our first solver, QMRES, maintains a set of clauses represented by a ZDD and eliminates quantifiers via multi-resolution. Our second solver, QBDD, maintains a set of OBDDs, and eliminate quantifier by applying them to the underlying OBDDs. We compare our symbolic solvers to several competitive search-based solvers. We show that QBDD is not competitive, but QMRES compares favorably with search-based solvers on various benchmarks consisting of non-random formulas.