The computational complexity of asymptotic problems I: Partial orders

The class of partial orders is shown to have 0-1 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 [infinity]. 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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27185/1/0000188.pd