Exact ASP Counting with Compact Encodings

TL;DR

This paper introduces sharpASP, a novel framework for exact answer set counting that leverages alternative definitions to improve scalability and performance over existing methods in ASP.

Contribution

It presents a new ASP counting approach that avoids large formulas and adapts propositional model counting techniques, significantly enhancing performance.

Findings

Solved 167 more benchmarks than previous methods.

Achieved a PAR2 score reduction from 4205 to 3082.

Demonstrated scalability on large benchmark sets.

Abstract

Answer Set Programming (ASP) has emerged as a promising paradigm in knowledge representation and automated reasoning owing to its ability to model hard combinatorial problems from diverse domains in a natural way. Building on advances in propositional SAT solving, the past two decades have witnessed the emergence of well-engineered systems for solving the answer set satisfiability problem, i.e., finding models or answer sets for a given answer set program. In recent years, there has been growing interest in problems beyond satisfiability, such as model counting, in the context of ASP. Akin to the early days of propositional model counting, state-of-the-art exact answer set counters do not scale well beyond small instances. Exact ASP counters struggle with handling larger input formulas. The primary contribution of this paper is a new ASP counting framework, called sharpASP, which counts answer sets avoiding larger input formulas. This relies on an alternative way of defining answer sets that allows for the lifting of key techniques developed in the context of propositional model counting. Our extensive empirical analysis over 1470 benchmarks demonstrates significant performance gain over current state-of-the-art exact answer set counters. Specifically, by using sharpASP, we were able to solve 1062 benchmarks with PAR2 score of 3082 whereas using prior state-of-the-art, we could only solve 895 benchmarks with a PAR2 score of 4205, all other experimental conditions being the same.