On sets truth-table reducible to sparse sets
SIAM Journal on Computing
Distinguishing conjunctive and disjunctive reducibilities by sparse sets
Information and Computation
On random reductions from sparse sets to tally sets
Information Processing Letters
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Separating Nondeterministic Time Complexity Classes
Journal of the ACM (JACM)
SPARSE Reduces Conjunctively to TALLY
SIAM Journal on Computing
Optimal Proof Systems for Propositional Logic and Complete Sets
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Survey of disjoint NP-pairs and relations to propositional proof systems
Theoretical Computer Science
Optimal Proof Systems, Optimal Acceptors and Recursive Presentability
Fundamenta Informaticae
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We exhibit a relativized world where NP ∩ SPARSE has no complete sets. This gives the first relativized world where no optimal proof systems exist. We also examine under what reductions NP ∩ SPARSE can have complete sets. We show a close connection between these issues and reductions from sparse to tally sets. We also consider the question as to whether the NP ∩ SPARSE languages have a computable enumeration.