... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400-variable 3-SAT problems in about 2 hours on the average. In general, it can solve hard n-variable random 3-SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NP-complete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.

We deal with directed hypergraphs as a tool to model and solve some classes of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented. Algorithms to perform visits of hypergraphs and to find optimal paths are studied in detail. Some applications arising in propositional logic, And-Or graphs, relational data bases and transportation analysis are presented. January 1990 Revised, October 1992 ( * ) This research has been supported in part by the "Comitato Nazionale Scienza e Tecnologia dell'Informazione", National Research Council of Italy, under Grant n.89.00208.12, and in part by research grants from the National Research Council of Canada. 1 Dipartimento di Informatica, Università di Pisa, Italy 2 Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Canada 2 INTRODUCTION Hypergraphs, a generaliz...

. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...

. We address methods of speeding up the calculation of the well-founded semantics for normal propositional logic programs. We first consider two algorithms already reported in the literature and show that these, plus a variation upon them, have much improved worst-case behavior for special cases of input. Then we propose a general algorithm to speed up the calculation for logic programs with at most two positive subgoals per clause, intended to improve the worst case performance of the computation. For a logic program P in atoms A, the speed up over the straight Van Gelder alternating fixed point algorithm (assuming worstcase behavior for both algorithms) is approximately (jPj=jAj) (1=3) . For jPj jAj 4 , the algorithm runs in time linear in jPj. 1 Introduction Logic programming researchers have, over the last several years, proposed many logic-based declarative semantics for various sorts of logic programming. The hope is that, if they can be efficiently implemented, t...

We describe the elds of disjunctive logic programming and disjunctive deductive databases from the time of their inception to the current time. Contributions with respect to semantics, implementations and applications are surveyed.

In the probabilistic analysis of algorithms for the Satisfiability problem, the random-clausewidth model is one of the most popular for generating random instances. This model is parameterized and it is not difficult to show that virtually the entire parameter space is covered by a collection of polynomial time algorithms that find solutions to random instances with probability tending to 1 as instance size increases. But finding a collection of polynomial average time algorithms that cover the parameter space has proved much harder and such results have spanned approximately ten years. However, it can now be said that virtually the entire parameter space is covered by polynomial average time algorithms. This paper relates dominant, exploitable properties of random formulas over the parameter space to mechanisms of polynomial average time algorithms. The probabilistic discussion of such properties is new; main average-case results over the last ten years are reviewed. 1 Intr...

this paper is in questions of decidability and tractability for open domain specifications -- open domain specifications using the finite open domain and arbitrarily large open domain hypotheses. For some corresponding results for the infinite open domain assumption we refer the reader to our paper [19]

We address a generalization of graphs, the directed hypergraphs, and show that they are a powerful tool in modelling and solving several relevant problems in many application areas. Such application areas include Linear Production Problems, Flexible Manufacturing Systems, Propositional Logic, Relational Databases, and Public Transportation Systems.

If a Horn set I has a single satisfying truth assignment or model then that model is said to be unique for I. The question of determining whether a unique model exists for a given Horn set I is shown to be solved in O(ff(L) L) time, where L is the sum of the lengths of the clauses in I and ff is the inverse Ackermann function. It is also shown that if L A log(A) where A is the number of distinct proposition letters then unique satisfiability can be determined in O(L) time. 1 Introduction Sets of Horn clauses are well-known to be computationally much more tractable than sets of arbitrary clauses. For example, satisfiability for sets of Horn clauses of propositional logic can be determined in linear time, whereas satisfiability for sets of arbitrary clauses of propositional logic is NP-hard. Unique satisfiability on Horn sets is one problem that can be solved in quadratic time [7] even though the general problem is co-NP hard [5]. Using ideas based on those of [7], we can improv...