Characterization of quadratic $\epsilon$-CNS polynomials (extended version)

In this paper, we give characterization of quadratic $\epsilon -$canonical number system ($\epsilon -$CNS) polynomials for all values $\epsilon \in [0,1)$. Our characterization provides a unified view of the well-known characterizations of the classical quadratic CNS polynomials ($\epsilon =0$) and quadratic SCNS polynomials ($\epsilon =1\mathrm{/}2$). This result is a consequence of our new characterization results of $\epsilon -$shift radix systems ($\epsilon -$SRS) in the two-dimensional case and their relation to quadratic $\epsilon -$CNS polynomials.