(Co)algebraic semantics of heavy-weighted automata
Marie C. Fortin, Marcello Bonsangue, Jan Rutten · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 2014
In this paper we study heavy-weighted automata, a generalization of weighted automata in which the weights of the transitions can be formal power series.As for ordinary weighted automata, the behaviour of heavy-weighted automata is expressed in terms of formal power series.We propose several equivalent definitions for their semantics, including a system of behavioural differential equations (following the approach of coinductive calculus), or an embedding into a coalgebra for the functor S × (-) A , for which the set of formal power series is a final coalgebra.Using techniques based on bisimulations and coinductive calculus, we study how ordinary weighted automata can be transformed into more compact heavy-weighted ones.