Skip to main content

Degrees and reducibilities of easy tally sets

  • Contributions
  • Conference paper
  • First Online:
Mathematical Foundations of Computer Science 1994 (MFCS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 841))

Abstract

The logarithmic advice class, Full-P/log, is known to coincide with the class of languages that are polynomial time reducible to special “easy” tally sets.

We study here how different resource-bounded reducibilities retrieve information encoded in these “easy” sets and we explain the relationships between the reducibilities and the equivalence classes defined from them.

This work was done while visiting LSI at UPC, and was partially supported by the ESPRIT EC project 7141 (ALCOM II).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allender, E., Rubinstein, R.: P-printable Sets. SIAM J. Comput. 17 (1988) 1193–1202

    Google Scholar 

  2. Allender, E., Watanabe, O.: Kolmogorov Complexity and Degrees of Tally Sets. Information and Computation. 86 (1990) 160–178

    Google Scholar 

  3. Balcázar, J.L., Book, R.: Sets with Small Generalized Kolmogorov Complexity. Acta Inform. 23 (1986) 679–688

    Google Scholar 

  4. Balcázar, J.L., Díaz, J., Gabarró, J.: Structural Complexity II. EATCS Monographs on Theoretical Computer Science. Vol. 22 (1990) Springer-Verlag

    Google Scholar 

  5. Balcázar, J.L., Gavaldà, R., Siegelmann, H.T., Sontag, E.D.: Some Structural Complexity Aspects of Neural Computation. In Proceedings of Structural in Complexity Theory 8th Annual Conference. IEEE Computer Society Press (1993) 253–265

    Google Scholar 

  6. Balcázar, J.L., Hermo, M., Mayordomo, E.: Characterizations of logarithmic advice complexity classes. In Proceedings of the IFIP 12th World Computer Congress. North-Holland Vol. 1 (1992) 315–321

    Google Scholar 

  7. Book, R., Ko, K.: On Sets Truth-Table Reducible to Sparse Sets. SIAM J. Comput. 17 (1988) 903–919

    Google Scholar 

  8. Balcázar, J.L., Schöning, U.: Logarithmic Advice Classes. Theoretical Computer Science. 99 (1992) 279–290

    Google Scholar 

  9. Hermo, M.: The Structure of a Logarithmic Advice Classes. Report LSI-93-30-R, Facultad de Informática de la UPC (1993)

    Google Scholar 

  10. Hartmanis, J., Hemachandra, L.: On Sparse Sets Separating Feasible Complexity Classes. Proceedings 3rd Annual Symposium on Theoretical Aspects of Computer Science. Lecture Notes in Computer Science. 210 (1996) 321–333

    Google Scholar 

  11. Karp, R.M., Lipton, R.J.: Some Connections Between Nonuniform and Uniform Complexity Classes. In Proceedings 12th Annual Symposium on Theory of Computing. (1980) 302–309

    Google Scholar 

  12. Ko, K.: Continuous Optimization Problems and Polynomial Hierarchy of Real Functions. J. Complexity. 1 (1985) 210–231

    Google Scholar 

  13. Ko, K.: On Helping by Robust Oracle Machines that Take Advice. Theoretical Computer Science. 52 (1987) 15–36

    Google Scholar 

  14. Köbler, J.: Untersuchung verschiedener polynomieller Reduktion Klassen von NP. Diplom. thesis, Institut für InformatiK, Univ. Stuttgart. (1985)

    Google Scholar 

  15. Siegelmann, H.T., Sontag E.D.: Neural Networks with Real Weights: Analog Computational Complexity. Report SYCON 92-05, Rutgers Center for Systems and Control. To appear in Theoretical Computer Science. (1993)

    Google Scholar 

  16. Tang, S., Book, R.: Reducibilities on Tally and Sparse Sets. Theoretical Informatics and Applications 25-3 (1991) 293–302

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Igor Prívara Branislav Rovan Peter Ruzička

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hermo, M. (1994). Degrees and reducibilities of easy tally sets. In: Prívara, I., Rovan, B., Ruzička, P. (eds) Mathematical Foundations of Computer Science 1994. MFCS 1994. Lecture Notes in Computer Science, vol 841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58338-6_87

Download citation

  • DOI: https://doi.org/10.1007/3-540-58338-6_87

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58338-7

  • Online ISBN: 978-3-540-48663-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics