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Journals ACM SIGACT News Volume 25 Issue 2

Complexity Theory Column 5 : The ot-Ready-For-Prime-Time Conjecture s Lane A . Hemaspaandr a Department of Computer Scienc e University of Rocheste r Rochester, NY 1462 7 lane@cs .rochester .ed u 1 Happy Hunting ! Summer! Time to slip away with a pad of paper and your favorite conjecture . In case you've ha d the good fortune of already resolving your favorite conjecture, or have had the bad luck to choos e a beastly favorite conjecture (e .g ., "Conjecture : NP NP coNP NP "), below are a few of my favorit e conjectures regarding complexity classes, along with some pointers towards relevant backgroun d papers . Happy hunting ! 2 Conjecture s 2 .1 Does P have Sparse Complete Sets ? Conjecture 1 No P-complete sets are sparse . Notation A set A is sparse if there exists a polynomial p( ¢) such that at each length n, A contains at most p(n) strings . The "P-complete" in the conjecture refers to completeness with respect t o logspace many-one reductions (as, if one were using polynomial-time reductions, one could use th e reduction to directly solve the problem) . Discussion The question of whether NP

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Complexity theory column 5: the not-ready-for-prime-time conjectures

Hemaspaandra, Lane A.
ACM SIGACT News , Volume 25 (2)
Association for Computing Machinery – Jun 1, 1994

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