ESO universal Horn formulae: machine level versus structure level hierarchy
Prabhu Manyem · arXiv (Cornell University) · 2011
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 Gradel (1991), is due to the fact that the expressions this paper deals with are at the structure level, whereas the expressions in Gradel (1991) are at the machine level --- a case of Easier done than said.