Skip to main content
SpringerLink
Log in

Predicatively computable functions on sets

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract

Inspired from a joint work by A. Beckmann, S. Buss and S. Friedman, we propose a class of set-theoretic functions, predicatively computable set functions. Each function in this class is polynomial time computable when we restrict to finite binary strings.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arai T., Moser G.: Proofs of Termination of Rewrite Systems for Polytime Functions. In: Ramanujam, R., Sen, S. (eds.) FSTTCS 2005: Foundations of software technology and theoretical computer science, pp.529–540. Lecture Notes in Compt. Sci. vol. 3821, Springer, Berlin (2005)

  2. Beckmann, A., Buss, S.R., Friedman, S.-D.: Safe recursive set functions (submitted)

  3. Bellantoni S., Cook S.: A new recursion-theoretic characterization of the polytime functions. Comput. Complex. 2, 97–110 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. Jensen R.: The fine structure of the constructible hierarchy. Ann. Math. Logic 4, 229–308 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  5. Jensen, R., Karp, C.: Primitive recursive set functions. In: Scott, D. (ed.) Axiomatic Set Theory, pp. 143–176. Proceedings of Symposia in Pure Mathematics, vol. 13, Part I, American Mathematical Society, Providence, RI (1971)

  6. Dal Lago, U., Martini, S., Zorzi, M.: General ramified recurrence is sound for polynomial time. In: Baillot, P. (ed.) Workshop on Developments in Implicit Complexity (DICE2010), pp. 47–62. EPTCS 23 (2010)

  7. Leivant, D.: Stratified functional programs and computational complexity. In: Proceedings of the 20th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 325–333. ACM (1993)

  8. Plump, D.: Term graph rewriting. In: Handbook of Graph Grammars and Computing by Graph Transformation, vol. 2, ch. 1, pp. 3–61. World Scientific, Singapore s(1999)

  9. Rathjen M.: A proof-theoretic characterization of the primitive recursive set functions. J. Symb. Logic 57, 954–969 (1992)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Science, Chiba University, 1-33, Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan

    Toshiyasu Arai

Authors
  1. Toshiyasu Arai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Toshiyasu Arai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arai, T. Predicatively computable functions on sets. Arch. Math. Logic 54, 471–485 (2015). https://doi.org/10.1007/s00153-015-0422-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-015-0422-2

Keywords

Mathematics Subject Classification

Search

Navigation