Towards an optimal separation of space and length in resolution

Jakob Nordström, Johan Håstad
2008 Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08  
Most state-of-the-art satisfiability algorithms today are variants of the DPLL procedure augmented with clause learning. The main bottleneck for such algorithms, other than the obvious one of time, is the amount of memory used. In the field of proof complexity, the resources of time and memory correspond to the length and space of resolution proofs. There has been a long line of research trying to understand these proof complexity measures, as well as relating them to the width of proofs, i.e.,
more » ... the size of a largest clause in the proof, which has been shown to be intimately connected with both length and space. While strong results have been proven for length and width, our understanding of space has been quite poor. For instance, it has remained open whether the fact that a formula is provable in short length implies that it is also provable in small space (which is the case for length versus width), or * A preliminary version of this paper appeared in the
doi:10.1145/1374376.1374478 dblp:conf/stoc/NordstromH08 fatcat:x2f4caw3rjhjhcho5vohx34o5u