Reference:
Matti Järvisalo. Impact of restricted branching on clause learning SAT solving. Research Report A107, Helsinki University of Technology, Laboratory for Theoretical Computer Science, Espoo, Finland, August 2007. ISBN 9789512289073.
Abstract:
Propositional satisfiability (SAT) solving procedures (or SAT solvers) are used as efficient backend search engines in solving industrialscale problems such as automated planning and verification. Typical SAT solvers are based on the DavisPutnamLogemannLoveland procedure (DPLL), which performs an intelligent depthfirst search over the solution space of a propositional logic formula. A key technique in SAT solvers is clause learning, which has been shown to make DPLL more efficient both theoretically and in practice. Branching heuristics, that is, deciding on which variable to next set a value during search, also plays an important role in the efficiency of search.
This report investigates the effect of structurebased branching restrictions on the efficiency of modern DPLL based SAT solvers with clause learning. Branching restrictions force the solver to restrict its decision making to a subset of the problem variables. Ideally, if the branching restriction consists of structurally important variables, the solver is guided to making relevant decisions, decreasing the time needed for solving the problem instance.
The contributions of the report are twofold. On one hand, a theoretical investigation of the effect of so called input restricted branching on the proof complexity theoretic efficiency of the proof system underlying DPLL based SAT solvers with clause learning is presented. It is shown that with input restricted branching, clause learning DPLL is polynomially incomparable with the standard DPLL. This implies that all implementations of clause learning DPLL, even with optimal heuristics, have the potential of suffering a notable efficiency decrease when input restricted branching is applied.
On the other hand, an extensive experimental evaluation of the effect of different structurebased branching restrictions on the practical efficiency of a stateoftheart clause learning DPLL implementation is provided. Compared to experimental evaluations found in the literature, the treatment is both deeper and wider: it is not limited to comparing running times and it provides more detailed experimental evidence for the reasons why input restricted branching has the potential of reducing search efficiency. The work also investigates the effect of restricting branching in a controlled way based on structural properties other than the plain input restriction.
Keywords:
Boolean circuits, branching heuristics, clause learning, constraint solving, DPLL, experimentation, problem structure, proof complexity, propositional satisfiability
Suggested BibTeX entry:
@techreport{HUTTCSA107,
address = {Espoo, Finland},
author = {Matti J\"arvisalo},
institution = {Helsinki University of Technology, Laboratory for Theoretical Computer Science},
month = {August},
note = {ISBN 9789512289073},
number = {A107},
pages = {viii+62},
title = {Impact of Restricted Branching on Clause Learning {SAT} Solving},
type = {Research Report},
year = {2007},
}
