Measuring the Hardness of SAT Instances

Carlos Ansótegui, Maria Luisa Bonet, Jordi Levy, Felip Manyà

Abstract:

The search of a precise measure of what hardness of SAT instances means for state-of-the-art solvers is a relevant research question. Among others, the space complexity of treelike resolution (also called hardness), the minimal size of strong backdoors and of cycle-cutsets, and the treewidth can be used for this purpose.

We propose the use of the tree-like space complexity as a solid candidate to be the best measure for solvers based on DPLL. To support this thesis we provide a comparison with the other mentioned measures. We also conduct an experimental investigation to show how the proposed measure characterizes the hardness of random and industrial instances.