Answer Set Counting and its Applications

TL;DR

This paper advances answer set programming by introducing both exact and approximate counting methods, with sharpASP and ApproxASP, which outperform existing tools and are applied to network reliability estimation.

Contribution

It presents novel exact and approximate answer set counters, sharpASP and ApproxASP, with improved efficiency and practical application to network reliability.

Findings

sharpASP outperforms existing ASP counters on benchmarks

ApproxASP provides efficient approximate counting using hashing and Gauss-Jordan elimination

ApproxASP achieves better network reliability estimates than traditional methods

Abstract

We have focused on Answer Set Programming (ASP), more specifically, answer set counting, exploring both exact and approximate methodologies. We developed an exact ASP counter, sharpASP, which utilizes a compact encoding for propositional formulas, significantly enhancing efficiency compared to existing methods that often struggle with inefficient encodings. Our evaluations indicate that sharpASP outperforms current ASP counters on several benchmarks. In addition, we proposed an approximate ASP counter, named ApproxASP, a hashing-based counter integrating Gauss-Jordan elimination within the ASP solver, clingo. As a practical application, we employed ApproxASP for network reliability estimation, demonstrating superior performance over both traditional reliability estimators and #SAT-based methods.