SOUR graphs for efficient completion

We introduce a data structure called \emphSOUR graphs and present an efficient Knuth-Bendix completion procedure based on it. \emphSOUR graphs allow for a maximal structure sharing of terms in rewriting systems. The term representation is a dag representation, except that edges are labelled with equational constraints and variable renamings. The rewrite rules correspond to rewrite edges, the unification problems to unification edges. The Critical Pair and Simplification inferences are recognized as patterns in the graph and are performed as local graph transformations. Our algorithm avoids duplicating term structure while performing inferences, which causes exponential behavior in the standard procedure. This approach gives a basis to design other completion algorithms, such as goal-oriented completion, concurrent completion and group completion procedures

A fine-grained concurrent completion procedure

Theme 2 - Genie logiciel et calcul symbolique. Projet PROTHEOSIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.1996 n.2990 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

A fine-grained Concurrent Completion Procedure

We present a concurrent Completion procedure based on the use of a SOUR graph as data structure. The procedure has the following characteristics. It is asynchronous, there is no need for a global memory or global control, equations are stored in a SOUR graph with maximal structure sharing, and each vertex is a process, representing a term. Therefore, the parallelism is at the term level. Each edge is a communication link, representing a (subterm, ordering, unification or rewrite) relation between terms. Completion is performed on the graph as local graph transformations by cooperation between processes. We show that this concurrent Completion procedure is sound and complete with respect to the sequential one, provided that the information is locally time stamped in order to detect out of date information