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Threshold machines are Turing machines whose acceptance is determined by what portion of the machine's computation paths are accepting paths. Probabilistic machines are Turing machines whose acceptance is determined by the probability weight of the machine's accepting computation paths. In 1975, Simon proved that for unbounded-error polynomial-time machines… (More)

In this paper we study the complexity of sets that reduce to sparse sets (and tally sets), and the complexity of the simplest sparse sets to which such sets reduce. We show even with respect to very exible reductions that NP cannot have sparse hard sets unless P = NP; an immediate consequence of our results is: If any NP-complete set conjunctively reduces… (More)

A semi-membership algorithm for a set <i>A</i> is, informally, a program that when given any two strings determines which is logically more likely to be in <i>A</i>. <i>A</i> flurry of interest in this topic in the late seventies and early eighties was followed by a relatively quiescent half-decade. However, in the 1990s there has been a resurgence of… (More)

- Junwook Kwak, Sechul Shin, Soohyun Kwon, Hochang Chae, Jeonghun Cho, Yunheung Paek +3 others
- ICOIN
- 2009

We investigate classes of sets that can be decided by bounded truth-table reductions to an NP set in which evaluators do not have full access to the answers to the queries but get only restricted information such as the number of queries that are in the oracle set or even just this number modulo m, for some m 2. We also investigate the case in which… (More)

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