Pointers in Recursion: Exploring the Tropics

Author Paulin Jacobé de Naurois

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Paulin Jacobé de Naurois
  • CNRS, Université Paris 13, Sorbonne Paris Cité, LIPN, UMR 7030, F-93430 Villetaneuse, France


I am grateful to the anonymous referees for their insightful and useful feedback.

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Paulin Jacobé de Naurois. Pointers in Recursion: Exploring the Tropics. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We translate the usual class of partial/primitive recursive functions to a pointer recursion framework, accessing actual input values via a pointer reading unit-cost function. These pointer recursive functions classes are proven equivalent to the usual partial/primitive recursive functions. Complexity-wise, this framework captures in a streamlined way most of the relevant sub-polynomial classes. Pointer recursion with the safe/normal tiering discipline of Bellantoni and Cook corresponds to polylogtime computation. We introduce a new, non-size increasing tiering discipline, called tropical tiering. Tropical tiering and pointer recursion, used with some of the most common recursion schemes, capture the classes logspace, logspace/polylogtime, ptime, and NC. Finally, in a fashion reminiscent of the safe recursive functions, tropical tiering is expressed directly in the syntax of the function algebras, yielding the tropical recursive function algebras.

Subject Classification

ACM Subject Classification
  • Software and its engineering → Recursion
  • Theory of computation → Complexity theory and logic
  • Theory of computation → Complexity classes
  • Implicit Complexity
  • Recursion Theory


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