Realization of Probabilistic Automata. Categorical Approach.
Paulo Mateus, Amflcar Sernadas, Cristina Sernadas · 2000
. We present a categorical framework to study probabilistic automata starting by obtaining aggregation and interconnection as universal constructions. We also introduce the notion of probabilistic behavior in order to get adjunctions between probabilistic behavior and probabilistic automata. Thus we are able to extend to the probabilistic setting free and minimal realizations as universal constructions. 1 Introduction Probabilistic automata [Rab63,Paz66] are central in the theory of unreliable systems, namely for providing the appropriate semantic domain (see for instance [BDEP97,LS91,vGSST95]). In particular we adopt the Moore model, that is, the outputs are assigned to the states. In [MSS99,SM99] we provided a (pre)categorical characterization for several combinations of probabilistic automata. However, we had to work with structures weaker than categories [Ehr65,Cop80] because composition of morphisms was not always dened. Herein we adopt a dierent approach by considering that th...