By Martin Gittins (auth.), A. Beaumont, G. Gupta (eds.)

Logic programming refers to execution of courses written in Horn common sense. one of the merits of this variety of programming are its uncomplicated declarativeand procedural semantics, excessive expressive strength and inherent nondeterminism. The papers integrated during this quantity have been provided on the Workshop on Parallel good judgment Programming held in Paris on June 24, 1991, as a part of the eighth overseas convention on good judgment Programming. The papers symbolize the state-of-the-art in parallel good judgment programming, and record the present examine during this region, together with many new effects. the 3 crucial matters in parallel execution of good judgment courses which the papers handle are: - Which form(s) of parallelism (or-parallelism, and-parallelism, circulate parallelism, data-parallelism, etc.) might be exploited? - Will parallelism be explicitly programmed through programmers, or will or not it's exploited implicitly with no their aid? - Which goal parallel structure will the common sense program(s) run on?

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**Extra resources for Parallel Execution of Logic Programs: ICLP '91 Pre-Conference Workshop Paris, June 24, 1991 Proceedings**

**Example text**

The left-hand sides of these two expressions are equal, therefore we can derive the relation \A\y < \R{A)\y. Since |A| > |i2(A)| holds, the only solution of the last inequation is y = 0. The right-haind side of each equation in S is equal to 0, therefore each variable x^ must also be 0. D The proof of the next lemma is quite straightforward. Lemma 2. For every perfect matching M in G, there exists a solution of the system S such that y = 1, x^ G {0,1}, and x^ = 1 if and only if e[ G M. Conversely, for every solution of S with y = 1 there exists a perfect matching in the bipartite graph G.

Durctnd. Personal communication, June 1999. [EE85] A. A. Elimcim and S. E. Elmaghraby. On the reduction method for integer linccir programs II. Discrete Applied Mathematics, 12(3):241-260, 1985. [Fag87] F. Fages. Associative commutative unification. Journal of Symbolic Computation, 3(3):257-275, 1987. [GJ79] M. R. Carey and D. S. Johnson. Computers and intractability: A guide to the theory of NP-completeness. H. Freeman and Co, 1979. [Gor73] P. Gordan. Ueber die Auflosung linearen Gleichungen mit reellen Coefficienten.

Lemma 5. Let S be a homogeneous linear Diophantine system over non-negative integers such that every variable has at most two occurrences. Then every minimal solution ( s i , . . ,s„) of S has the property that the value of each coefficient Si is at most 2. Proof. (Hint) The main idea of the proof is to transform the system S and a given solution s into a graph having the following property: each cycle in the graph represents a new solution s' such that s' is either the trivial all-zero solution or it is a solution that is pointwise smaller than or equal to the original solution s.