The Infinite Versions of LogSpace ≠ P Are Consistent with the Axioms of Set Theory
We consider the infinite versions of the usual computational complexity questions LogSpace ≟ P, NLogSpace ≟ P by studying the comparison of their descriptive logics on infinite partially ordered structures rather than restricting ourselves to finite structures. We show that the infinite versions of those famous class separation questions are consistent with the axioms of set theory and we give a sufficient condition on the complexity classes in order to get other such relative consistency results.
KeywordsPartial Order Point Operator Turing Machine Complexity Class Logical Description
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