Expressibility at the machine level versus structure level: ESO universal Horn Logic and the class P
Abstract
We show that ESO universal Horn logic (existential second logic where the first order part is a universal Horn formula) is insufficient to capture P, the class of problems decidable in polynomial time. This statement is true in the presence of a successor relation in the input vocabulary. We provide two proofs --- one based on reduced products of two structures, and another based on approximability theory (the second proof is under the assumption that P is not the same as NP). We show that the difference between the results here and those in Gr\"{a}del (1991), is due to the fact that the expressions this paper deals with are at the "structure level", whereas the expressions in Gr\"{a}del (1991) are at the "machine level" --- a case of Easier done than said.
Cite
@article{arxiv.1106.4606,
title = {Expressibility at the machine level versus structure level: ESO universal Horn Logic and the class P},
author = {Prabhu Manyem},
journal= {arXiv preprint arXiv:1106.4606},
year = {2012}
}