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J. Fichte, M. Hecher, M. Morak, S. Woltran:
"Exploiting Treewidth for Projected Model Counting and Its Limits";
Talk: Theory and Applications of Satisfiability Testing - (SAT), Oxford, UK; 2018-07-09 - 2018-07-12; in: "Theory and Applications of Satisfiability Testing - (SAT 2018) - 21st International Conference, (SAT 2018)Held as Part of the Federated Logic Conference, FloC 2018, Oxford, UK, July 9-12, 2018, Proceedings", Springer, (2018), ISBN: 978-3-319-94143-1; 165 - 184.

In this paper, we introduce a novel algorithm to solve projected model counting (PMC). PMC asks to count solutions of a Boolean formula with respect to a given set of projected variables, where multiple solutions that are identical when restricted to the projected variables count as only one solution. Our algorithm exploits small treewidth of the primal graph of the input instance. It runs in time O(22k+4n2) where k is the treewidth and n is the input size of the instance. In other words, we obtain that the problem PMC is fixed-parameter tractable when parameterized by treewidth. Further, we take the exponential time hypothesis (ETH) into consideration and establish lower bounds of bounded treewidth algorithms for PMC, yielding asymptotically tight runtime bounds of our algorithm.

Parameterized algorithms; Tree decompositions; Multi-pass dynamic programming; Projected model counting; Propositional logic

http://dx.doi.org/10.1007/978-3-319-94144-8_11

https://publik.tuwien.ac.at/files/publik_273224.pdf

Project Head Reinhard Pichler:
Effiziente, parametrisierte Algorithmen in Künstlicher Intelligenz und logischem Schließen

Project Head Stefan Woltran:
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