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Electronic Colloquium on Computational Complexity

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Reports tagged with DPLL:
TR06-140 | 8th November 2006
Paul Beame, Russell Impagliazzo, Nathan Segerlind

Formula Caching in DPLL

We consider extensions of the DPLL approach to satisfiability testing that add a version of memoization, in which formulas that the algorithm has previously shown to be unsatisfiable are remembered for later use. Such formula caching algorithms have been suggested for satisfiability and stochastic satisfiability. We formalize these methods by ... more >>>

TR12-141 | 22nd October 2012
Dmitry Itsykson, Dmitry Sokolov

Lower bounds for myopic DPLL algorithms with a cut heuristic

The paper is devoted to lower bounds on the time complexity of DPLL algorithms that solve the satisfiability problem using a splitting strategy. Exponential lower bounds on the running time of DPLL algorithms on unsatisfiable formulas follow from the lower bounds for resolution proofs. Lower bounds on satisfiable instances are ... more >>>

TR17-117 | 20th July 2017
Dmitry Itsykson, Alexander Knop

Hard satisfiable formulas for splittings by linear combinations

Itsykson and Sokolov in 2014 introduced the class of DPLL($\oplus$) algorithms that solve Boolean satisfiability problem using the splitting by linear combinations of variables modulo 2. This class extends the class of DPLL algorithms that split by variables. DPLL($\oplus$) algorithms solve in polynomial time systems of linear equations modulo two ... more >>>

TR18-117 | 23rd June 2018
Fedor Part, Iddo Tzameret

Resolution with Counting: Lower Bounds over Different Moduli

Revisions: 2

Resolution over linear equations (introduced in [RT08]) emerged recently as an important object of study. This refutation system, denoted Res(lin$_R$), operates with disjunction of linear equations over a ring $R$. On the one hand, the system captures a natural ``minimal'' extension of resolution in which efficient counting can be achieved; ... more >>>

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