Abstract
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.
Cite
CITATION STYLE
Buhrman, H., Fenner, S., Fortnow, L., & van Melkebeek, D. (2000). Optimal proof systems and sparse sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1770, pp. 407–418). Springer Verlag. https://doi.org/10.1007/3-540-46541-3_34
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