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Isomorphisms and 1-L reductions

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Book cover Structure in Complexity Theory

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 223))

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

  1. E. W. Allender, Invertible functions, Doctoral Dissertation, Georgia Institute of Technology.

    Google Scholar 

  2. E. W. Allender, The complexity of sparse sets in P, These Proceedings.

    Google Scholar 

  3. L. Berman, Polynomial reducibilities and complete sets, Doctoral Dissertation, Cornell University.

    Google Scholar 

  4. L. Berman and J. Hartmanis, On isomorphisms and density of NP and other complete sets, SIAM J. Comput. 6, 305–323.

    Google Scholar 

  5. M. Dowd, Isomorphism of complete sets, Technical Report LCSR-TR-34, Rutgers University.

    Google Scholar 

  6. J. Hartmanis, N. Immerman, and S. Mahaney, One-way log-tape reductions, Proc. 19th IEEE Symposium on Foundations of Computer Science, pp. 65–72.

    Google Scholar 

  7. J. Hartmanis and S. Mahaney, Languages simultaneously complete for one-way and two-way log-tape automata, SIAM J. Comput. 10, 383–390.

    Google Scholar 

  8. J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, Mass.

    Google Scholar 

  9. D. T. Huynh, Non-uniform complexity and the randomness of certain complete languages, Technical Report TR 85-34, Computer Science Department, Iowa State University.

    Google Scholar 

  10. 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.

    Google Scholar 

  11. K.-I. Ko, T. J. Long, and D.-Z. Du, A note on one-way functions and polynomial-time isomorphisms, to appear.

    Google Scholar 

  12. S. Mahaney and P. Young, Reductions among polynomial isomorphism types, Theoretical Computer Science 39, 207–224.

    Google Scholar 

  13. L. J. Stockmeyer, The complexity of decision problems in automata theory and logic, Doctoral Dissertation, M.I.T.

    Google Scholar 

  14. Osamu Watanabe, On one-one polynomial time equivalence relations, Theoretical Computer Science 38, 157–165.

    Google Scholar 

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Alan L. Selman

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16486-9

  • Online ISBN: 978-3-540-39825-7

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