Itsykson and Sokolov in 2014 introduced the class of DPLL(⊕) 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(⊕) algorithms solve in polynomial time systems of linear equations modulo 2 that are hard for DPLL, PPSZ and CDCL algorithms. Itsykson and Sokolov have proved first exponential lower bounds for DPLL(⊕) algorithms on unsatisfiable formulas. In this paper we consider a subclass of DPLL(⊕) algorithms that arbitrary choose a linear form for splitting and randomly (with equal probabilities) choose a value to investigate first; we call such algorithms drunken DPLL(⊕). We give a construction of a family of satisfiable CNF formulas Ψn of size poly(n) such that any drunken DPLL(⊕) algorithm with probability at least 1-2-Ω(n) runs at least 2Ω(n) steps on Ψn; thus we solve an open question stated in the paper [12]. This lower bound extends the result of Alekhnovich, Hirsch and Itsykson [1] from drunken DPLL to drunken DPLL(⊕).
CITATION STYLE
Itsykson, D., & Knop, A. (2017). Hard satisfiable formulas for splittings by linear combinations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10491 LNCS, pp. 53–61). Springer Verlag. https://doi.org/10.1007/978-3-319-66263-3_4
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