Polynomial models of the final determined automatic devices above a field $GF(2^p)$.

Method of modeling the finite deterministic automaton (FDA) as a homogeneous computational structure in $GF(2^p)$ is examined. The method is based on configuration of homogeneous structure which consists of similar blocks. The idea of this configuration is based on representing functions of FDA as polynomial in $GF(2^p)$. Possibility of changing polynomial model of FDA with memory and without output is researched in case of representing it as polynomial of one variable in Galua field.