Geodesic
On the equality problem of finitely generated classes of exponentially-polynomial functions
Diskretnaya Matematika, Tome 34 (2022) no. 1, pp. 64-75

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We consider the class $\mathrm{EP}_{\mathbb N}$ of exponentially-polynomial functions which can be obtained by arbitrary superpositions of the constants 0, 1 and arithmetic operations of addition, multiplication, and powering. For this class, we solve the algorithmic equality problem of two functions that assume a finite number of values. Next, this class is restricted to the class $\mathrm{PEP}_{\mathbb N}$, in which the function $x^y$ is replaced by a sequence of functions $\{p_i^x\}$, where $p_0, p_1,\ldots$ are all prime numbers. For the class $\mathrm{PEP}_{\mathbb N}$, the problem of membership of a function to a finitely generated class is effectively reduced to the equality problem of two functions. In turn, the last problem is effectively solved for the set of all one-place $\mathrm{PEP}_{\mathbb N}$-functions.
Keywords: exponentially-polynomial functions, equality problem. 
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     author = {S. S. Marchenkov},
     title = {On the equality problem of finitely generated classes of exponentially-polynomial functions},
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     pages = {64--75},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2022_34_1_a4/}
}
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S. S. Marchenkov. On the equality problem of finitely generated classes of exponentially-polynomial functions. Diskretnaya Matematika, Tome 34 (2022) no. 1, pp. 64-75. http://geodesic.mathdoc.fr/item/DM_2022_34_1_a4/