Abstract:
The basic properties of polynomially stable Boolean functions are examined. We prove that any polynomially stable function can be represented as the sum of terms that are nonrepetitive in an elementary basis. Relationships between polynomially stable and symmetric Boolean functions are discussed and a criterion for polynomial stability is proved.
Keywords:operator for Boolean functions, Zhegalkin polynomial, repetition-free formula, polynomial stability, symmetric Boolean function, weight of a binary set.
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