The Good Old Davis-Putnam Procedure Helps Counting Models
Abstract
As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F. Let m and n be the number of clauses and variables of F, respectively, and let p denote the probability that a literal l of F occurs in a clause C of F, then the average running time of CDP is shown to be O(mdn), where d=[-1/log2(1-p)].The practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas.
Cite
Text
Birnbaum and Lozinskii. "The Good Old Davis-Putnam Procedure Helps Counting Models." Journal of Artificial Intelligence Research, 1999. doi:10.1613/JAIR.601Markdown
[Birnbaum and Lozinskii. "The Good Old Davis-Putnam Procedure Helps Counting Models." Journal of Artificial Intelligence Research, 1999.](https://mlanthology.org/jair/1999/birnbaum1999jair-good/) doi:10.1613/JAIR.601BibTeX
@article{birnbaum1999jair-good,
title = {{The Good Old Davis-Putnam Procedure Helps Counting Models}},
author = {Birnbaum, Elazar and Lozinskii, Eliezer L.},
journal = {Journal of Artificial Intelligence Research},
year = {1999},
pages = {457-477},
doi = {10.1613/JAIR.601},
volume = {10},
url = {https://mlanthology.org/jair/1999/birnbaum1999jair-good/}
}