Diminution: On Reducing the Size of Grounding ASP Programs

TL;DR

This paper introduces the concept of diminution, a formal method to reduce the Herbrand universe in ASP, leading to significant improvements in grounding efficiency and size reduction.

Contribution

It formalizes the notion of diminution, analyzes its properties, and provides a practical encoding for integrating with existing ASP grounders.

Findings

Grounding time reduced by up to 70%

Grounding file size decreased by up to 85%

Effective across multiple benchmark problems

Abstract

Answer Set Programming (ASP) is often hindered by the grounding bottleneck: large Herbrand universes generate ground programs so large that solving becomes difficult. Many methods employ ad-hoc heuristics to improve grounding performance, motivating the need for a more formal and generalizable strategy. We introduce the notion of diminution, defined as a selected subset of the Herbrand universe used to generate a reduced ground program before solving. We give a formal definition of diminution, analyze its key properties, and study the complexity of identifying it. We use a specific encoding that enables off-the-shelf ASP solver to evaluate candidate subsets. Our approach integrates seamlessly with existing grounders via domain predicates. In extensive experiments on five benchmarks, applying diminutions selected by our strategy yields significant performance improvements, reducing grounding time by up to 70% on average and decreasing the size of grounding files by up to 85%. These results demonstrate that leveraging diminutions constitutes a robust and general-purpose approach for alleviating the grounding bottleneck in ASP.