On Polynomial Representations of Boolean Functions Related to Some Number Theoretic Problems
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
Polynomials that Sign Represent Parity and Descartes' Rule of Signs
Computational Complexity
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We investigate the complexity of Boolean functions f with respect to realizations by real polynomials p (voting polynomials) in the sense that the sign of p(x) determines the value f(x). Considerable research has been done on determining the minimal degree needed for realizing or approximating particular functions. In this paper we focus our interest on estimating the minimal number of monomials, i.e. the length of realizing polynomials. Our main observation is that, in contrast to the degree, the minimal length essentially depends on whether we realize f over the domain.