General Ramified Recurrence is Sound for Polynomial Time

Details General Ramified Recurrence is Sound for Polynomial Time General Ramified Recurrence is Sound for Polynomial Time

2010-05-04

arxiv.org/abs/1005.0521v1

EPTCS 23, 2010, pp. 47-62

Computer Science

Logic in Computer Science

Scientific paper

10.4204/EPTCS.23.4

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.

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