TY - GEN

T1 - On one query, self-reducible sets

AU - Ogiwara, Mitsunori

AU - Lozano, Antoni

PY - 1991/12/1

Y1 - 1991/12/1

N2 - The authors study one-word-decreasing self-reducible sets, which are the usual self-reducible sets with the peculiarity that the self-reducibility machine makes at most one query to a word lexicographically smaller than the input. It is first shown that for all counting classes defined by a predicate on the number of accepting paths there exist complete sets which are one-word-decreasing self-reducible. Using this fact it is proved that, for any class K chosen from a certain set of complexity classes, it holds that (1) if there is a sparse polynomial-time bounded-truth-table-hard set for K, then K = P, and (2) if there is a sparse strongly nondeterministic bounded-truth-table-hard set for K, then K ⊂ NP 23 co-NP. The main result also shows that the same facts hold for the class PSPACE.

AB - The authors study one-word-decreasing self-reducible sets, which are the usual self-reducible sets with the peculiarity that the self-reducibility machine makes at most one query to a word lexicographically smaller than the input. It is first shown that for all counting classes defined by a predicate on the number of accepting paths there exist complete sets which are one-word-decreasing self-reducible. Using this fact it is proved that, for any class K chosen from a certain set of complexity classes, it holds that (1) if there is a sparse polynomial-time bounded-truth-table-hard set for K, then K = P, and (2) if there is a sparse strongly nondeterministic bounded-truth-table-hard set for K, then K ⊂ NP 23 co-NP. The main result also shows that the same facts hold for the class PSPACE.

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M3 - Conference contribution

AN - SCOPUS:0026398367

SN - 0818622555

T3 - Proc 6 Annu Struct Complexity Theor

SP - 139

EP - 151

BT - Proc 6 Annu Struct Complexity Theor

PB - Publ by IEEE

T2 - Proceedings of the 6th Annual Structure in Complexity Theory Conference

Y2 - 30 June 1991 through 3 July 1991

ER -