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Precategories for Combining Probabilistic Automata

✍ Scribed by Paulo Mateus; Amílcar Sernadas; Cristina Sernadas

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
802 KB
Volume
29
Category
Article
ISSN
1571-0661

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✦ Synopsis

A relaxed notion of category is presented having in mind the categorical caracterization of the mechanisms for combining probabilistic automata, since the composition of the appropriate morphisms is not always de ned. A detailed discussion of the required notion of morphism is provided. The partiality of composition of such morphisms is illustrated at the abstract level of countable probability spaces. The relevant fragment of the theory of the proposed precategories is developed, including (constrained) products and Cartesian liftings. Precategories are precisely placed in the universe of neocategories. Some classical results from category theory are shown to carry over to precategories. Other results are shown not to hold in general. As an application, the precategorical universal constructs are used for characterizing the basic mechanisms for combining probabilistic automata: aggregation, interconnection and state constraining.

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