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On the effect of variable identification on the essential arity of functions

Miguel Couceiro·Erkko Lehtonen
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Abstract

We show that every function of several variables on a finite set of k elements with n>k essential variables has a variable identification minor with at least n-k essential variables. This is a generalization of a theorem of Salomaa on the essential variables of Boolean functions. We also strengthen Salomaa's theorem by characterizing all the Boolean functions f having a variable identification minor that has just one essential variable less than f.

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Miguel Couceiro, Erkko Lehtonen. 2007-01-11. On the effect of variable identification on the essential arity of functions. https://doi.org/10.1142/s012905410700508x

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