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A minimal substitution basis for the Kalmár elementary functions
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DOI：10.1093/logcom/exag010.png)
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Abstract
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We show that the class of Kalm & aacute;r elementary functions can be inductively generated from the addition, the integer remainder and the base-two exponentiation, hence improving previous results by Marchenkov and Mazzanti. We also prove that the substitution basis defined by these three operations is minimal. Furthermore, we discuss alternative substitution bases under arity constraints.
Keywords:
arithmetic term
closed form
elementary function
elementary operation
explicit formula
Grzegorczyk's hierarchy
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