Equivalence relations, invariants, and normal forms
SIAM Journal on Computing
Journal of the ACM (JACM)
Proceedings of the Mathematical Foundations of Computer Science 1984
On Relativization and the Existence of Complete Sets
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Containment, Separation, Complete Sets, and Immunity of Complexity Classes
ICALP '86 Proceedings of the 13th International Colloquium on Automata, Languages and Programming
Algebrization: a new barrier in complexity theory
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
ICDT'05 Proceedings of the 10th international conference on Database Theory
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In a paper published in 1988, Yuri Gurevich gave a precise mathematical formulation of the central question in descriptive complexity - is there a logic capturing P - and conjectured that the answer is no. In the same paper, he also conjectured that there was no logic capturing either of the complexity classes NP ∩ co-NP and RP, and presented evidence for these conjectures based on the construction of oracles with respect to which these classes do not have complete problems. The connection between the existence of complete problems and the existence of a logic capturing P was further established in (Dawar 1995). Does this imply that the question of whether there is a logic capturing P is subject to a relativization barrier? Here, we examine this question and see how the question for P differs from those for the other classes by taking a short tour through relativizations, complete problems and recursive enumerations of complexity classes.