The computational complexity of asymptotic problems I: Partial orders

Kevin J. Compton
1988 Information and Computation  
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
more » ... f 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 fatcat:nd272a33kvg3th4jygy4k3y5ku