General Ramified Recurrence is Sound for Polynomial Time

Ugo Dal Lago
Simone Martini
Margherita Zorzi

Leivant's ramified recurrence is one of the earliest examples of an implicit characterization of the polytime functions as a subalgebra of the primitive recursive functions. Leivant's result, however, is originally stated and proved only for word algebras, i.e. free algebras whose constructors take at most one argument. This paper presents an extension of these results to ramified functions on any free algebras, provided the underlying terms are represented as graphs rather than trees, so that sharing of identical subterms can be exploited.

In Patrick Baillot: Proceedings International Workshop on Developments in Implicit Computational complExity (DICE 2010), Paphos, Cyprus, 27-28th March 2010, Electronic Proceedings in Theoretical Computer Science 23, pp. 47–62.
Published: 5th May 2010.

ArXived at: http://dx.doi.org/10.4204/EPTCS.23.4 bibtex PDF

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