To each one-dimensional subshift $X$, we may associate a winning shift $W(X)$ which arises from combinatorial game played on the language of $X$. Previously it has been studied what properties $X$ does inherit. For example, and have same factor complexity if is sofic subshift, then also sofic. In this paper, develop notion automaticity for $W(X)$, that is, propose means vector representation ac...

Abstract We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.