## Counting Models for 2SAT and 3SAT Formulae

Citations: | 5 - 0 self |

### BibTeX

@MISC{Dahllöf_countingmodels,

author = {Vilhelm Dahllöf and Peter Jonsson and Magnus Wahlström},

title = {Counting Models for 2SAT and 3SAT Formulae},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

We here present algorithms for counting models and max-weight models for 2sat and 3sat formulae. They use polynomial space and run in O(1.2561^n) and O(1.6737^n) time, respectively, where n is the number of variables. This is faster than the previously best algorithms for counting non-weighted models for 2sat and 3sat, which run in O(1.3247^n) and O(1.6894^n) time, respectively. In order to prove these time bounds, we develop new measures of formula complexity, allowing us to conveniently analyze the eoeects of certain factors with a large impact on the total running time. We also provide an algorithm for the restricted case of separable 2sat formulae, with fast running times for well-studied input classes. For all three algorithms we present interesting applications, such as computing the permanent of sparse 0/1 matrices.