Paul Young
- [BBJSY-89] Bertoni, A., D. Bruschi, D. Joseph, M. Sitharam, and P. Young, "Generalized Boolean hierarchies and Boolean hierarchies over RP," final version prior to publication available as Univ Wisc CS Tech Report; short abstract in Proc. 7th Symp Foundations Computing Theory, (FCT- 1989), Springer-Verlag, LNCS 380, 35-46.Google Scholar
- [CGHHSWW-88] J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung, "The Boolean hierarchy I: structural properties," SIAM J Comput., 6 (1988), 1232-1252. Google ScholarDigital Library
- [CGHHSWW-89] J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung, "The Boolean hierarchy II: applications," SIAM J Comput, 7 (1989), 95-111. Google ScholarDigital Library
- [HL-91] S. Homer and L. Longpré, "On reductions of NP sets to sparse sets," Structure in Complexity Conference, 6 (1991), 79-88.Google Scholar
- [OW-91] M. Ogiwara and O. Watanabe. "On polynomial-time bounded truth-table reducibility of NP sets to sparse sets," SIAM Journal on Computing, 20(3) (1991), 471-483. Google ScholarDigital Library
- [Uk-83] E. Ukkonen, "Two results on polynomial time truth-table reductions to sparse sets," SIAM J Comput, 12 (1983), 580-587.Google ScholarCross Ref
- [Wa-87] O. Watanabe, "Polynomial time reducibility to a set of small density," Structure in Complexity Conference, (1987), 138-146.Google Scholar
- [Wa-88] O. Watanabe, "On ¿1-ttP-sparseness and nondeterministic complexity classes," ICALP, (1988), 697-709. Google ScholarDigital Library
- [Ya-83] C. Yap, "Some consequences of non-uniform conditions on uniform classes," Theor Comput Sci 26 (1983), 287-300.Google ScholarCross Ref
- [Ye-83] Y. Yesha, "On certain polynomial time truth-table reductions to sparse sets," SIAM J Comput, 12 (1983), 411-425.Google ScholarCross Ref
- [AHHKLMOSST-92] V. Arvind, et al., "Reductions to sets of low information content," Technical Report, University of Rochester, C.S. Dept., 417 (April, 1992), 1-54.Google ScholarCross Ref
- [AKM-92] V. Arvind, J. Köbler, and M. Mundhenk, "Bounded truth-table and conjunctive reductions to sparse and tally sets," Technical Report, Universität Ulm Fakultät für Informatik, 92-01 (April, 1992), 1-22.Google Scholar
- [Bi-92] Bin Fu, "With quasi-linear queries, EXP is not polynomial time Turing reducible to sparse sets," Preprint, Beijing Computer Institute, (1992), 1-11.Google Scholar
- [BLS-92] H. Buhrman, Luc Longpré, and Edith Spaan, "Sparse reduces conjunctively to tally," Technical Report, Northeastern University, NU-CCS-92-8 (1992), 1-11.Google Scholar
- [RR-92] D. Ranjan and P. Rohatgi, "Randomized reductions to sparse sets," Proceedings 7th Structure in Complexity Theory Conference 7 (1992), to appear.Google Scholar
- [Yo-92] P. Young, "How Reductions to Sparse Sets Collapse the Polynomial Time Hierarchy: A Primer. Part I: Polynomial-time Turing Reductions," SIGACT News, 23 (3) (1992), 107-117. Google ScholarDigital Library
Index Terms
- How reductions to sparse sets collapse the polynomial-time hierarchy: a primer: Part II restricted polynomial-time reductions
Recommendations
Two Results on Polynomial Time Truth-Table Reductions to Sparse Sets
Inspired by the recent solution of the Berman-Hartmanis conjecture [SIAM J. Comp., 6 (1977), pp. 305–322] that NP cannot have a sparse complete set for many-one reductions unless ${\text{P}} = {\text{NP}}$, we analyze the implications of NP and PSPACE ...
On reductions of NP sets to sparse sets
Ogiwara and Watanabe showed that if SAT is bounded truth-table reducible to a sparse set, then P = NP. In this paper we simplify their proof, strengthen the result and use it to obtain several new results. Among the new results are the following:*...
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