Electronic version of an article published as International Journal of Foundations of Computer Science 18(5) (2007) 975-986. DOI: 10.1142/S012905410700508X. © copyright World Scientific Publishing Company, http://www.worldscientific.com/worldscinet/ijfcs.
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Abstract :
[en] 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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