Abstract

The class \(\textrm{EP}_{\mathbb{N}}\) of all exponential-polynomial functions that can be obtained from the functions \(0,1,x+y,x\cdot y,\) and \(x^{y}\) by arbitrary superpositions is considered. In \(\textrm{EP}_{\mathbb{N}}\), six precomplete (with respect to the superposition operation) classes are efficiently defined so that a completeness criterion and a recognition algorithm for completeness are formulated in their base for finite systems of functions.

中文翻译：

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一类指数多项式函数的完备性判据

摘要

所有指数多项式函数的类\（\ textrm {EP} _ {\ mathbb {N}} \）可以从函数\（0,1，x + y，x \ cdot y，\）和\（x ^ {y} \）被认为是任意叠加。在\（\ textrm {EP} _ {\ mathbb {N}} \）中，有效地定义了六个预完成（相对于叠加操作）类，以便在其基础上制定完整性准则和用于完整性的识别算法，以用于功能的有限系统。