Finitely Ambiguous and Finitely Sequential Weighted Automata over Fields

Abstract

Expressive power of finitely ambiguous and finitely sequential weighted automata over fields is examined. Rational series realised by such automata can be classified into infinite hierarchies according to ambiguity and sequentiality degrees of realising automata – it is shown that both these hierarchies are strict already over unary alphabets in case the field under consideration is not locally finite. Moreover, the expressive power of finitely sequential, finitely ambiguous, and polynomially ambiguous weighted automata is compared over different fields, both for unary and arbitrary finite alphabets, drawing a complete picture of the relations between corresponding classes of formal power series.