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Theory and Applications of Satisfiability Testing – SAT by Nadia Creignou, Daniel Le Berre

By Nadia Creignou, Daniel Le Berre

This ebook constitutes the refereed court cases of the nineteenth foreign convention on idea and functions of Satisfiability checking out, SAT 2016, held in Bordeaux, France, in July 2016.

The 31 average papers, five software papers awarded including three invited talks have been rigorously reviewed and chosen from 70 submissions. The papers tackle various facets of SAT, together with complexity, satisfiability fixing, satisfiability purposes, satisfiability modulop idea, past SAT, quantified Boolean formulation, and dependency QBF.

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Extra info for Theory and Applications of Satisfiability Testing – SAT 2016: 19th International Conference, Bordeaux, France, July 5-8, 2016, Proceedings

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Model counting for CNF formulas of bounded modular treewidth. , Wilke, T. ) 30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013, Kiel, Germany, 27 February–2 March 2013. LIPIcs, vol. 20, pp. 55–66. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2013) 20. : No small nondeterministic read-once branching programs for CNFs of bounded treewidth. , Heggernes, P. ) IPEC 2014. LNCS, vol. 8894, pp. 319–331. Springer, Heidelberg (2014) 21. : On OBDDs for CNFs of bounded treewidth.

3. Let P m,n be the pigeonhole picture. 1 determines in time O(m4 · n4 ) whether P m,n has a (π, V, H)-solution. In case such a solution exists the algorithm constructs it. Proof. 2, P m,n is O(m · n)-smooth. Additionally, the extension number of (π, V ) is e(π, V ) = 3. 6, we can construct each automaton Ai,j (P m,n , π, V, H) in time at most O(m3 · n3 ). Since there are m · n such automata, the whole algorithm takes time at most O(m4 · n4 ). 6 From Pictures to Constant Width CNF Formulas Let π : Σ → Γ be a function, V, H ⊆ Σ × Σ be binary relations over Σ, and M be an m × n-picture over Γ .

6 Connections to Model Counting and Affine Decision Trees In this section we discuss connections of the findings of this paper to practical model counting. It has been shown that there is a tight connection between compilation and model counting, as runs of exhaustive DPLL-based model counting algorithms can be translated into (restricted) DNNFs [14]. Here the size of the resulting DNNF corresponds to the runtime of the model counter. Since state of the art solvers like Cachet [23] and sharpSAT [24] use exhaustive DPLL, the lower bounds in this paper can be seen as lower bounds for these programs: model counting for CNF formulas of size n and, modular treewidth will take 10 S.

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