Abstract
Following the impressive progress made in the quest for efficient SAT solving in the last years, a number of researches has focused on explaining performances observed on typical application problems. However, until now, tentative explanations were only partial, essentially because the semantic of the original problem was lost in the translation to SAT.
In this work, we study the behavior of so called “modern” SAT solvers under the prism of the first successful application of CDCL solvers, i.e., Bounded Model Checking. We trace the origin of each variable w.r.t. its unrolling depth, and show a surprising relationship between these time steps and the communities found in the CNF encoding. We also show how the VSIDS heuristic, the resolution engine, and the learning mechanism interact with the unrolling steps. Additionally, we show that the Literal Block Distance (LBD), used to identify good learnt clauses, is related to this measure.
Our work shows that communities identify strong dependencies among the variables of different time steps, revealing a structure that arises when unrolling the problem, and which seems to be caught by the LBD measure.
This work was partially supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement no. 279611, and by the French National Research Agency (ANR), with the ANR SATAS Project 2015 (ANR-15-CE40-0017-01), and SafeRiver.
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Notes
- 1.
CDCL is nowadays the dominant technique solving this kind of problems.
- 2.
In this model, the variables of the CNF are the nodes of the graph, and there is an edge between two variables if they appear together in a clause. In its weighted version –the one we use–, the clause size is also considered.
- 3.
For simplicity, we omit the very few variables which do not belong to any iteration.
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Baud-Berthier, G., Giráldez-Cru, J., Simon, L. (2017). On the Community Structure of Bounded Model Checking SAT Problems. In: Gaspers, S., Walsh, T. (eds) Theory and Applications of Satisfiability Testing – SAT 2017. SAT 2017. Lecture Notes in Computer Science(), vol 10491. Springer, Cham. https://doi.org/10.1007/978-3-319-66263-3_5
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