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Exponential lower bounds for the running time of DPLL algorithms on satisfiable formulas #

Summary: Exponential lower bounds for the running time
of DPLL algorithms on satisfiable formulas #
Michael Alekhnovich 1 ## , Edward A. Hirsch 2 # # # , and Dmitry Itsykson 3+
1 Institute for Advanced Study, Princeton, USA, misha@ias.edu
2 St.Petersburg Department of Steklov Institute of Mathematics, St. Petersburg,
191011, Russia, hirsch@pdmi.ras.ru
3 Faculty of Mathematics and Mechanics, St.Petersburg State University,
St.Petersburg, Russia, dmitrits@mail.ru
Abstract. DPLL (for Davis, Putnam, Logemann, and Loveland) algo­
rithms form the largest family of contemporary algorithms for SAT (the
propositional satisfiability problem) and are widely used in applications.
The recursion trees of DPLL algorithm executions on unsatisfiable formu­
las are equivalent to tree­like resolution proofs. Therefore, lower bounds
for tree­like resolution (which are known since 1960s) apply to them.
However, these lower bounds say nothing about the behavior of such
algorithms on satisfiable formulas. Proving exponential lower bounds for
them in the most general setting is impossible without proving P #= NP;
therefore, in order to prove lower bounds one has to restrict the power of
branching heuristics. In this paper, we give exponential lower bounds for
two families of DPLL algorithms: generalized myopic algorithms (that


Source: Alekhnovich, Michael - Institute for Advanced Study, Princeton University


Collections: Mathematics; Computer Technologies and Information Sciences