Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0741.68049
Ogiwara, Mitsunori; Watanabe, Osamu
On polynomial-time bounded truth-table reducibility of NP sets to sparse sets. (English)
[J] SIAM J. Comput. 20, No.3, 471-483 (1991). ISSN 0097-5397; ISSN 1095-7111/e

For each reduction type $r$, the concept of ``$\leq\sp P\sb r$- reducibility to sparse sets'' indicates a certain tractability notion. There are several types of polynomial time reductions $r$: $\leq\sp P\sb T$ (Turing reduction), $\leq\sp P\sb m$ (many-one reduction), $\leq\sp P\sb{k-tt}$ ($k$-truth-table reduction), $\leq\sp P\sb{btt}$ ( bounded truth-table reduction), etc. It is known that:\par (i) a set has polynomial size circuits iff it is $\leq\sp P\sb T$- reducible to a sparse set, and\par (ii) if $P\ne NP$ then no $NP$-complete set is $\leq\sp P\sb m$-reducible to a sparse set.\par The aim of this paper is to extend this last result to $\leq\sp P\sb{btt}$-reducibility (which is more general than $\leq\sp P\sb T$- reducibility). It is proved that if $P\ne NP$ then $NP$ has a set which is not $\leq\sp P\sb{btt}$-reducible to any sparse set. It is also mentioned that the same technique allows one to prove that several number-theoretic problems (such as a factorization problem) either are in $P$ or are not $\leq\sp P\sb{btt}$-reducible to any sparse set, i.e., either these problems are tractable or are ``hardly'' intractable.
[S.P.Yukna (Vilnius)]

MSC 2000:: *68Q15 Complexity classes of computation
03D15 Complexity of computation
03D30 Degrees, other than r.e.

Keywords: Berman-Hartmanis conjecture; polynomial-time hard sets; sparse sets; bounded truth-table reduction

Cited in: Zbl 0780.68043

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]