Formal series over sorted algebras Original Research Article

We define two types of series over Σ-algebras: formal series and, as a special case, term series. By help of term series we define systems (of equations) that have tuples of formal series as solutions. We then introduce finite automata and polynomial systems and show that they are mechanisms of equal power. Morphisms from formal series into power series yield combinatorial results. Moreover, we prove a Kleene Theorem.