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Expressibility at the machine level versus structure level: ESO universal Horn Logic and the class P
[article]
2012
arXiv
pre-print
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
arXiv:1106.4606v5
fatcat:sttu6s2o2be6pd2y7yxazeknmu