Proceedings Fifth Annual Structure in Complexity Theory Conference
Two aspects of the structure of complete sets for NE and larger nondeterministic time classes are... more Two aspects of the structure of complete sets for NE and larger nondeterministic time classes are surveyed. First, differences between complete sets arising from various polynomial-time reductions are proved. Immunity properties of these complete sets are then considered. It is shown that NE-complete sets (and their complements) have dense E subsets and dense UP subsets. All of these results hold
It is shown that determining whether a quantum computation has a non-zero probability of acceptin... more It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation. 1
Abstract. We study the problem of finding a hidden code k in the domain (1,..., my* in the presen... more Abstract. We study the problem of finding a hidden code k in the domain (1,..., my* in the presence of an oracle which, for any z in the domain, answers a pair of numbers a(z, k) and b(z, k) such that a(z, k) is the number of components coinciding in z and k and, b(z, k) is the sum of ...
The existence of minimal degrees is investigated for several polynomial reducibilities. It is sho... more The existence of minimal degrees is investigated for several polynomial reducibilities. It is shown that no set has minimal degree with respect to polynomial many-one or Turing reducibility. This extends a result of Ladner in which only recursive sets are considered. A polynomial reducibility ≤<supscrpt><italic>h</italic></supscrpt><subscrpt><italic>T</italic></subscrpt> is defined. This reducibility is a strengthening of polynomial Turing reducibility, and its properties relate to the P = ? NP question. For this new reducibility, a set of minimal degree is constructed under the assumption that P = NP. However, the set constructed is nonrecursive, and it is shown that no recursive set is of minimal ≤ <supscrpt><italic>h</italic></supscrpt><subscrpt><italic>T</italic></subscrpt> degree.
Proceedings Fifth Annual Structure in Complexity Theory Conference
Two aspects of the structure of complete sets for NE and larger nondeterministic time classes are... more Two aspects of the structure of complete sets for NE and larger nondeterministic time classes are surveyed. First, differences between complete sets arising from various polynomial-time reductions are proved. Immunity properties of these complete sets are then considered. It is shown that NE-complete sets (and their complements) have dense E subsets and dense UP subsets. All of these results hold
It is shown that determining whether a quantum computation has a non-zero probability of acceptin... more It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation. 1
Abstract. We study the problem of finding a hidden code k in the domain (1,..., my* in the presen... more Abstract. We study the problem of finding a hidden code k in the domain (1,..., my* in the presence of an oracle which, for any z in the domain, answers a pair of numbers a(z, k) and b(z, k) such that a(z, k) is the number of components coinciding in z and k and, b(z, k) is the sum of ...
The existence of minimal degrees is investigated for several polynomial reducibilities. It is sho... more The existence of minimal degrees is investigated for several polynomial reducibilities. It is shown that no set has minimal degree with respect to polynomial many-one or Turing reducibility. This extends a result of Ladner in which only recursive sets are considered. A polynomial reducibility ≤<supscrpt><italic>h</italic></supscrpt><subscrpt><italic>T</italic></subscrpt> is defined. This reducibility is a strengthening of polynomial Turing reducibility, and its properties relate to the P = ? NP question. For this new reducibility, a set of minimal degree is constructed under the assumption that P = NP. However, the set constructed is nonrecursive, and it is shown that no recursive set is of minimal ≤ <supscrpt><italic>h</italic></supscrpt><subscrpt><italic>T</italic></subscrpt> degree.
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