Completeness Criterion in Class of Exponential-Polynomial Functions

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.