Relativized limitations of left set technique and closure classes of sparse sets

A number of theorems are proved by introducing the notion of k-families of sets of strings, and an algorithm which outputs the sets of certain k-families is given. The algorithm is used to disjunctively reduce the left set (or 1wdsr set) to a sparse set. The set output by the algorithm on an input corresponds to the set queried by the disjunctive reduction on the input.<<ETX>>

[1]  Juris Hartmanis,et al.  On Isomorphisms and Density of NP and Other Complete Sets , 1977, SIAM J. Comput..

[2]  Osamu Watanabe,et al.  Relating equivalence and reducibility to sparse sets , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[3]  Noam Nisan,et al.  Hardness vs. randomness , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[4]  Ker-I Ko,et al.  On Sets Truth-Table Reducible to Sparse Sets , 1988, SIAM J. Comput..

[5]  Chee-Keng Yap,et al.  Some Consequences of Non-Uniform Conditions on Uniform Classes , 1983, Theor. Comput. Sci..

[6]  Richard J. Lipton,et al.  Some connections between nonuniform and uniform complexity classes , 1980, STOC '80.

[7]  Edith Hemaspaandra,et al.  SPARSE reduces conjunctively to TALLY , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.

[8]  Yaacov Yesha,et al.  On Certain Polynomial-Time Truth-Table Reducibilities of Complete Sets to Sparse Sets , 1983, SIAM J. Comput..

[9]  Hans Heller,et al.  On Relativized Exponential and Probabilistic Complexity Classes , 1986, Inf. Control..

[10]  Vikraman Arvind,et al.  On Bounded Truth-Table, Conjunctive, and Randomized Reductions to Sparse Sets , 1992, FSTTCS.

[11]  R.E. Ladner,et al.  A Comparison of Polynomial Time Reducibilities , 1975, Theor. Comput. Sci..

[12]  Ker-I Ko.  Distinguishing Conjunctive and Disjunctive Reducibilities by Sparse Sets , 1989, Inf. Comput..

[13]  Esko Ukkonen.  Two Results on Polynomial Time Truth-Table Reductions to Sparse Sets , 1983, SIAM J. Comput..

[14]  Mitsunori Ogihara,et al.  On one query, self-reducible sets , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[15]  S. Homer,et al.  On reductions of NP sets to sparse sets , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[16]  Lane A. Hemaspaandra,et al.  Reductions to Sets of Low Information Content , 1992, Complexity Theory: Current Research.

[17]  Osamu Watanabe,et al.  On polynomial time bounded truth-table reducibility of NP sets to sparse sets , 1990, STOC '90.

[18]  Osamu Watanabe,et al.  On Polynomial-Time Bounded Truth-Table Reducibility of NP Sets to Sparse Sets , 1991, SIAM J. Comput..

[19]  Jim Kadin,et al.  P^(NP[O(log n)]) and Sparse Turing-Complete Sets for NP , 1989, J. Comput. Syst. Sci..

[20]  Uwe Schöning,et al.  Complexity and Structure , 1986, Lecture Notes in Computer Science.

[21]  Stephen R. Mahaney.  Sparse Complete Sets of NP: Solution of a Conjecture of Berman and Hartmanis , 1982, J. Comput. Syst. Sci..