Generalizing the Order of Goals as an Approach to Generalizing Number

Abstract

The common idea among previous approaches for generalizing number is to look for repeated applications of rules (or operators) while generalizing an example proof to produce a general schema. We describe another approach, the algorithm N, that generalizes number from planning problems which are stated in the STRIPS-formalism. Instead of generalizing the structure of an example proof in terms of operator applications, the algorithm generalizes the order in which the literals in the goal state description are reached, yielding a generalized precedence graph. The algorithm N is compared to one of the previous approaches for generalizing number, that can be applied to planning problems which are stated in the STRIPS-formalism. Experiments have shown that schemata produced by algorithm N can be more efficiently utilized than schemata produced by the previous algorithm. Also, the algorithm N is shown to be able to handle a class of problems that the previous algorithm cannot.