Abstract
All sets complete for NP under 1-L reductions are complete under length-increasing, invertible, and “almost one-one” ≤ p m reductions. All sets complete for PSPACE under 1-L reductions are p-isomorphic.
Portions of this research were carried out while the author was supported by NSF grant MCS 81-03608.
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References
E. W. Allender, Invertible functions, Doctoral Dissertation, Georgia Institute of Technology.
E. W. Allender, The complexity of sparse sets in P, These Proceedings.
L. Berman, Polynomial reducibilities and complete sets, Doctoral Dissertation, Cornell University.
L. Berman and J. Hartmanis, On isomorphisms and density of NP and other complete sets, SIAM J. Comput. 6, 305–323.
M. Dowd, Isomorphism of complete sets, Technical Report LCSR-TR-34, Rutgers University.
J. Hartmanis, N. Immerman, and S. Mahaney, One-way log-tape reductions, Proc. 19th IEEE Symposium on Foundations of Computer Science, pp. 65–72.
J. Hartmanis and S. Mahaney, Languages simultaneously complete for one-way and two-way log-tape automata, SIAM J. Comput. 10, 383–390.
J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, Mass.
D. T. Huynh, Non-uniform complexity and the randomness of certain complete languages, Technical Report TR 85-34, Computer Science Department, Iowa State University.
D. Joseph and P. Young, Some remarks on witness functions for non-polynomial and non-complete sets in NP, Theoretical Computer Science 39, 225–237.
K.-I. Ko, T. J. Long, and D.-Z. Du, A note on one-way functions and polynomial-time isomorphisms, to appear.
S. Mahaney and P. Young, Reductions among polynomial isomorphism types, Theoretical Computer Science 39, 207–224.
L. J. Stockmeyer, The complexity of decision problems in automata theory and logic, Doctoral Dissertation, M.I.T.
Osamu Watanabe, On one-one polynomial time equivalence relations, Theoretical Computer Science 38, 157–165.
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© 1986 Springer-Verlag Berlin Heidelberg
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Allender, E.W. (1986). Isomorphisms and 1-L reductions. In: Selman, A.L. (eds) Structure in Complexity Theory. Lecture Notes in Computer Science, vol 223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16486-3_86
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DOI: https://doi.org/10.1007/3-540-16486-3_86
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