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- W2114529219 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." @default.
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- W2114529219 date "2004-01-01" @default.
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- W2114529219 title "Counting Complexity of Solvable Black-Box Group Problems" @default.
- W2114529219 doi "https://doi.org/10.1137/s0097539703420651" @default.
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