The Computational Complexity of Asymptotic Problems I: Partial Orders

Abstract

The class of partial orders is shown to have Ol laws for first-order logic and for inductive fixed-point logic, a logic which properly contains first-order logic. This means that for every sentence in one of these logics the proportion of labeled (or unlabeled) partial orders of size n satisfying the sentence has a limit of either 0 or 1 as n goes to co. This limit, called the asymptotic probability of the sentence, is the same for labeled and unlabeled structures. The computational complexity of the set of sentences with asymptotic probability 1 is determined. For first-order logic, it is PSPACE-complete. For inductive fixed-point logic, it is EXPTIME-complete.

DOI: 10.1016/0890-5401(88)90032-6

Cite this paper

@article{Compton1988TheCC, title={The Computational Complexity of Asymptotic Problems I: Partial Orders}, author={Kevin J. Compton}, journal={Inf. Comput.}, year={1988}, volume={78}, pages={108-123} }