Evaluating Answer Set Programming with Non-Convex Recursive Aggregates

Issue title: Special issue of the 22nd RCRA International Workshop on “Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion”

Guest editors: Stefano Bistarelli, Andrea Formisano, Marco Maratea and Paolo Torroni

Article type: Research Article

Authors: Alviano, Mario^{a; *}

Affiliations: [a] Department of Mathematics and Computer Science, University of Calabria, Via Pietro Bucci 30/B, 87036 Rende (CS), Italy. [email protected]

Correspondence: [*] Address for correspondence: Department of Mathematics and Computer Science, Via Pietro Bucci 30/B, 87036 Rende (CS), Italy.

Abstract: Aggregation functions are widely used in answer set programming (ASP) for representing and reasoning on knowledge involving sets of objects collectively. These sets may also depend recursively on the results of the aggregation functions, even if so far the support for such recursive aggregations was quite limited in ASP systems. In fact, recursion over aggregates was restricted to convex aggregates, i.e., aggregates that may have only one transition from false to true, and one from true to false, in this specific order. Recently, such a restriction has been overcome, so that the user can finally use non-convex recursive aggregates in ASP programs. An evaluation of ASP programs with non-convex recursive aggregates is reported in this paper, also testing a recently proposed extension of the concept of the positive extension graph to the case of programs with aggregates. Moreover, as an additional contribution, new rewritings for EVEN and ODD are presented: EVEN maps to true aggregation sets containing an even number of true literals, and ODD maps to true aggregation sets containing an odd number of true literals. Both aggregates are non-convex, and previously replaced by a conjunction of non-convex sums, whose size is quadratic with respect to the number of literals in the aggregation set. A different rewriting is presented in this paper, whose size is linear with respect to the number of literals in the aggregation set.

Keywords: answer set programming, aggregation functions, non-convex recursive aggregates

DOI: 10.3233/FI-2016-1441

Journal: Fundamenta Informaticae, vol. 149, no. 1-2, pp. 1-34, 2016