Backdoor DNFs

Stefan Szeider

Abstract: We introduce backdoor DNFs, as a tool to measure the theoretical hardness of CNF formulas. Like backdoor sets, backdoor DNFs are defined relative to a tractable class of CNF formulas. Each con- junctive term of a backdoor DNF defines a partial assignment which moves the input CNF formula into the base class. Backdoor DNFs are more expressive and potentially smaller than its prede- cessors backdoor sets and backdoor trees. We es- tablish the fixed-parameter tractability of the back- door DNF detection problem. Our result holds for the fundamental base classes Horn and 2CNF, and their combination. We complement our theoretical findings by an empirical study. Our experiments show that backdoor DNFs provide a significant im- provement over their predecessors.