General Ramified Recurrence is Sound for Polynomial Time

Q4 Economics, Econometrics and Finance
Ugo Dal Lago, S. Martini, M. Zorzi
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引用次数: 11

Abstract

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.
一般分支递归对多项式时间是可靠的
黎凡特的分支递归是最早将多时函数作为原始递归函数的子代数进行隐式表征的例子之一。然而,Leivant的结果最初只被表述和证明为词代数,即其构造函数最多有一个参数的自由代数。本文将这些结果推广到任意自由代数上的分支函数,只要底层项被表示为图而不是树,这样就可以利用相同子项的共享。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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CESifo DICE Report
CESifo DICE Report Economics, Econometrics and Finance-Economics and Econometrics
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