p4 is a portable library of C and Fortran subroutines for programming parallel computers. It is the current version of a system that has been in use since 1984. It includes features for explicit parallel programming of shared-memory machines, distributed-memory machines (including heterogeneous networks of workstations), and clusters, by which we mean sharedmemory multiprocessors communicating via message passing. We discuss here the design goals, history, and system architecture of p4 and describe briefly a diverse collection of applications that have demonstrated the utility of p4. 1 Introduction p4 is a library of routines designed to express a wide variety of parallel algorithms portably, efficiently and simply. The goal of portability requires it to use widely accepted models of computation rather than specific vendor implementations of those models. The goal of efficiency requires it to use models of computation relatively close to those provided by the machines themselves and t...

This article addresses the problem of indexing and retrieving first-order predicate calculus terms in the context of automated deduction programs. The four retrieval operations of concern are to find variants, generalizations, instances, and terms that unify with a given term. Discrimination-tree indexing is reviewed, and several variations are presented. The path-indexing method is also reviewed. Experiments were conducted on large sets of terms to determine how the properties of the terms affect the performance of the two indexing methods. Results of the experiments are presented.

In this paper we show that distributing the theorem proving task to several experts is a promising idea. We describe the team work method which allows the experts to compete for a while and then to cooperate. In the cooperation phase the best results derived in the competition phase are collected and the less important results are forgotten. We describe some useful experts and explain in detail how they work together. We establish fairness criteria and so prove the distributed system to be both, complete and correct. We have implemented our system and show by non-trivial examples that drastical time speed-ups are possible for a cooperating team of experts compared to the time needed by the best expert in the team.

We present a parallel completion procedure for term rewriting systems. Despite an extensive literature concerning the well-known sequential Knuth-Bendix completion procedure, little attention has been devoted to designing parallel completion procedures. Because naive parallelizations of sequential procedures lead to over-synchronization and poor performance, we employ a transition-based approach that enables more effective parallelizations. The approach begins with a formulation of the completion procedure as a set of transitions (in the style of Bachmair, Dershowitz, and Hsiang) and proceeds to a highly tuned parallel implementation that runs on a shared memory multiprocessor. The implementation performs well on a number of standard examples.

We present a very simple parallel execution model suitable for inference systems with nondeterministic choices (OR-branching points). All the parallel processors solve the same task without any communication. Their programs only differ in the initialization of the random number generator used for branch selection in depth first backtracking search. This model, called random competition, permits us to calculate analytically the parallel performance for arbitrary numbers of processors. This can be done exactly and without any experiments on a parallel machine. Finally, due to their simplicity, competition architectures are easy (and therefore low-priced) to build. As an application of this systematic approach we compute speedup expressions for specific problem classes defined by their run-time distributions. The results vary from a speedup of 1 for linearly degenerate search trees up to clearly "superlinear" speedup for strongly imbalanced search trees. Moreover, we are able to give esti...

We present an asynchronous MIMD algorithm for Grobner basis computation. The algorithm is based on the well-known sequential algorithm of Buchberger. Two factors make the correctness of our algorithm nontrivial: the nondeterminism that is inherent with asynchronous parallelism, and the distribution of data structures which leads to inconsistent views of the global state of the system. We demonstrate that by describing the algorithm as a nondeterministic sequential algorithm, and presenting the optimized parallel algorithm through a series of refinements to that algorithm, the algorithm is easier to understand and the correctness proof becomes manageable. The proof does, however, rely on algebraic properties of the polynomials in the computation, and does not follow directly from the proof of Buchberger's algorithm.