Abstract: "This paper studies the class of infinite sets that have minimal perfect hash functions -- one-to-one onto maps between the sets and [sigma]* -- computable in polynomial time. We show that all standard NP-complete sets have polynomial-time computable minimal perfect hash functions, an...

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Bibliographic Details

Main Authors:	Goldsmith, Judy (Author), Hemachandra, Lane A. (Author), Kunen, Kenneth (Author)
Format:	Book
Language:	English
Published:	Rochester, NY 1990
Series:	University of Rochester <Rochester, NY> / Department of Computer Science: Technical report 339
Subjects:	Computational complexity Set theory
Summary:	Abstract: "This paper studies the class of infinite sets that have minimal perfect hash functions -- one-to-one onto maps between the sets and [sigma]* -- computable in polynomial time. We show that all standard NP-complete sets have polynomial-time computable minimal perfect hash functions, and give a structural condition sufficient to ensure that all infinite NP sets have polynomial-time computable minimal perfect hash functions: If [formula], then all infinite NP sets have polynomial-time computable minimal perfect hash functions On the other hand, we present evidence that some infinite NP sets, and indeed some infinite P sets, do not have polynomial-time computable minimal perfect hash functions: if an infinite NP set A has polynomial-time computable perfect minimal hash functions, then A has an infinite sparse NP subset, yet we construct a relativized world in which some infinite NP sets lack infinite sparse NP subsets. This world is built upon a result that is of interest in its own right; we determine optimally -- with respect to any relativizable proof technique -- the complexity of the easiest infinite sparse subsets that infinite P sets are guaranteed to have.
Physical Description:	16 S.