Efficiency and Completeness of the Set of Support Strategy in Theorem Proving
Journal of the ACM (JACM)
State-space problem-reduction, and theorem proving—some relationships
Communications of the ACM
A geometric analysis of heuristic search
AFIPS '76 Proceedings of the June 7-10, 1976, national computer conference and exposition
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Previous studies of heuristic search techniques have usually considered situations for which the search space could be represented as a tree, which limits the applicability of the results obtained. Here Kowalski is followed and a more general formulation in terms of derivation graph is offered; the graphs correspond rather naturally to the search problems arising in automatic theoremproving and other areas. We consider a family of search procedures controlled by evaluation functions of a very general sort, having the form ƒDgr;(x, Lk), where Lk is that portion of the graph generated thus far by the procedure, and the node x is a candidate for incorporation into Lk. Completeness and minimality results are obtained for a number of procedures in this family, including methods analogous to those of Moore, Dijkstra, and Pohl.