The power of non-ground rules in Answer Set Programming

Abstract

Answer set programming (ASP) is a well-established logic programming language that offers an intuitive, declarative syntax for problem solving. In its traditional application, a fixed ASP program for a given problem is designed and the actual instance of the problem is fed into the program as a set of facts This approach typically results in programs with comparably short and simple rules However, as is known from complexity analysis, such an approach limits the expressive power of ASP; in fact, an entire NP-check can be encoded into a single large rule body of bounded arity that performs both a guess and a check within the same rule Here, we propose a novel paradigm for encoding hard problems in ASP by making explicit use of large rules which depend on the actual instance of the problem. We illustrate how this new encoding paradigm can be used, providing examples of problems from the first, second, and even third level of the polynomial hierarchy As state-of-the-art solvers are tuned towards short rules, rule decomposition is a key technique in the practical realization of our approach We also provide some preliminary benchmarks which indicate that giving up the convenient way of specifying a fixed program can lead to a significant speed-up. This paper is under consideration for acceptance in TPLP.

Constraints, lazy constraints, or propagators in ASP solving: An empirical analysis

“…As far as future work is concerned, we will study what are the conditions under which an entire subprogram (and not just some constraints) can be replaced by a propagator. Another line of research might be to investigate the impact of applying rule decomposition techniques before handling the constraints (Bichler et al 2016).…”

selp: A Single-Shot Epistemic Logic Program Solver

“…However, this approach was not implemented, and only presented as an example to show how long non-ground rules with fixed arity can be used to solve hard problems. In order to use such encodings (including our own presented herein), (Bichler et al 2016b) make use of rule decomposition, where large non-ground ASP rules are split up into smaller parts based on tree decompositions (Morak and Woltran 2012). This rule decomposition approach has been implemented as a stand-alone tool called lpopt (Bichler et al 2016a), but has recently also been integrated into ASP solving systems like I-DLV (Calimeri et al 2017).…”

Very Hard Electoral Control Problems

“…Despite its limitations, our encoding is an important starting point for future optimization and comparison of techniques. In particular, we are interested in how techniques for overcoming the grounding bottleneck such as rewriting large rules [7] can improve the performance of our encoding.…”