Abstract
Encoding finite linear CSPs as Boolean formulas and solving them by using modern SAT solvers has proven to be highly effective by the award-winning sugar system. We here develop an alternative approach based on ASP that serves two purposes. First, it provides a library for solving CSPs as part of an encompassing logic program. Second, it furnishes an ASP-based CP solver similar to sugar. Both tasks are addressed by using first-order ASP encodings that provide us with a high degree of flexibility, either for integration within ASP or for easy experimentation with different implementations. When used as a CP solver, the resulting system aspartame re-uses parts of sugar for parsing and normalizing CSPs. The obtained set of facts is then combined with an ASP encoding that can be grounded and solved by off-the-shelf ASP systems. We establish the competitiveness of our approach by empirically contrasting aspartame and sugar.
This paper is a greatly revised version of the workshop paper [1]. The work was funded by \(^1\)AoF (251170), \(^6\)DFG (SCHA 550/10-1), \(^5\)5\(\,\times \,\)1000 (UNIFE 2011), and \(^3\)JSPS (KAKENHI 15K00099).
T. Schaub–Affiliated with Simon Fraser University, Canada, and IIIS Griffith University, Australia.
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Notes
- 1.
- 2.
- 3.
When used as CP solver, aspartame re-uses sugar’s front-end for parsing and normalizing (non-linear) CSPs. Also, we extended sugar to produce a fact-based representation.
- 4.
This will be integrated into gringo’s input language in the near future.
- 5.
Linear and non-linear inequalities relying on further comparison operators, such as \(<\), \(>\), \(\ge \), \(=\), and \(\ne \), can be converted into the considered format via appropriate replacements [5]. Moreover, note that we here limit the constraints to the ones that are directly, i.e., without normalization by sugar, supported in our prototypical ASP encodings shipped with aspartame.
- 6.
- 7.
- 8.
The timeouts of sugar during translation are always due to insufficient memory.
- 9.
The system is available at http://www.cs.uni-potsdam.de/aspartame/.
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Banbara, M. et al. (2015). aspartame: Solving Constraint Satisfaction Problems with Answer Set Programming. In: Calimeri, F., Ianni, G., Truszczynski, M. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2015. Lecture Notes in Computer Science(), vol 9345. Springer, Cham. https://doi.org/10.1007/978-3-319-23264-5_10
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