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A Recursion-Theoretic Characterisation of the Positive Polynomial-Time Functions

Authors Anupam Das, Isabel Oitavem

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Author Details

Anupam Das
  • University of Copenhagen, Denmark
Isabel Oitavem
  • CMA and DM, FCT, Universidade Nova de Lisboa, Portugal

Funding

  • Das, Anupam: This work was supported by a Marie Skłodowska-Curie fellowship, Monotonicity in Logic and Complexity, ERC project 753431.
  • Oitavem, Isabel: This work is partially supported by the Portuguese Science Foundation, FCT, through the projects UID/MAT/00297/2013 and PTDC/MHC-FIL/2583/2014.

Cite As Get BibTex

Anupam Das and Isabel Oitavem. A Recursion-Theoretic Characterisation of the Positive Polynomial-Time Functions. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.CSL.2018.18

Abstract

We extend work of Lautemann, Schwentick and Stewart [Clemens Lautemann et al., 1996] on characterisations of the "positive" polynomial-time predicates (posP, also called mP by Grigni and Sipser [Grigni and Sipser, 1992]) to function classes. Our main result is the obtention of a function algebra for the positive polynomial-time functions (posFP) by imposing a simple uniformity constraint on the bounded recursion operator in Cobham's characterisation of FP. We show that a similar constraint on a function algebra based on safe recursion, in the style of Bellantoni and Cook [Stephen Bellantoni and Stephen A. Cook, 1992], yields an "implicit" characterisation of posFP, mentioning neither explicit bounds nor explicit monotonicity constraints.

Subject Classification

ACM Subject Classification
  • Theory of computation → Recursive functions
Keywords
  • Monotone complexity
  • Positive complexity
  • Function classes
  • Function algebras
  • Recursion-theoretic characterisations
  • Implicit complexity
  • Logic

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