NDLI: On the Accepting Density Hierarchy in NP

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Moran, Shlomo
Copyright Year	1982
Abstract	Let $Al$ be a polynomial time nondeterministic algorithm accepting a set A, and let $a \in A$. The accepting density of $Al$ for a is the ratio between the number of accepting computations and the total number of computations of $Al$ on input a. (If this ratio is $ \geqq 1/2$ for all $a \in A$, then $Al$ is a polynomial time probabilistic algorithm accepting A.)In this paper a characterization of sets in NP according to their accepting density is investigated. It is shown that for some relativized form of NP no general, nontrivial lower bound on the accepting density of sets in NP exists. It follows that for this relativized form the accepting density of any NP complete set for inputs of length n cannot be greater than $1/2^{n^c } $ for some fixed $c > 0$ and that NP (under that relativization) can be partitioned to infinitely many classes $C_1 ,C_2 , \cdots $, such that the accepting density of sets in $C_i $ is strictly greater, in some precise sense, than that of sets in $C_{i + 1} $. Recent works on the relationship between relativized and unrelativized proof techniques imply that to prove that any of the above results does not hold for the (unrelativized) class NP, possible at all, is probably beyond the ability of todays techniques.
Starting Page	344
Ending Page	349
Page Count	6
File Format	PDF
ISSN	00975397
DOI	10.1137/0211026
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	2
Volume Number	11
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	P NP probabilistic algorithms nondeterministic algorithms algorithms with oracles
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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