NDLI: Counting Complexity of Solvable Black-Box Group Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Vinodchandran, N. V.
Copyright Year	2004
Abstract	We place many computational problems over solvable black-box groups in the counting complexity classes SPP or LWPP\@. The classes SPP and LWPP are considered classes of low counting complexity. In particular, SPP is low (powerless when used as oracles) for all gap-definable counting classes (PP\@, C$_=$P\@, Mod$_k$P\@, etc.) and LWPP is low for PP and C$_=$P\@. The results improve the upper bounds for these problems proved in [Arvind and Vinodchandran, Theoret. Comput. Sci., 180 (1997), pp. 17--45], where the authors place these problems in randomized versions of SPP and LWPP. Because of the randomization, upper bounds in that paper implied lowness only for the class PP. The results in this paper favor the belief that these problems are unlikely to be complete for NP.
Starting Page	852
Ending Page	869
Page Count	18
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539703420651
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	33
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2004-01-01
Access Restriction	Subscribed
Subject Keyword	Computational difficulty of problems computational complexity theory complexity classes computational group theory Complexity classes
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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Counting Complexity of Solvable Black-Box Group Problems