Abstract and concrete categories
Abstract and concrete categories
Endomorphism spectra of graphs
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Reactive, generative, and stratified models of probabilistic processes
Information and Computation
Handbook of logic in computer science (vol. 4)
Composition and behaviors of probabilistic I/O automata
Theoretical Computer Science
On the Power of Finite Automata with both Nondeterministic and Probabilistic States
SIAM Journal on Computing
Communicating sequential processes
Communications of the ACM
Non-determinism and uncertainty in the situation calculus
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Data Encapsulation and Modularity: Three Views of Inheritance
MFCS '93 Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science
Categorical foundations for randomly timed automata
Theoretical Computer Science
Paracategories II: adjunctions, fibrations and examples from probabilistic automata theory
Theoretical Computer Science
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Frequently, mathematical structures of a certain type and their morphisms fail to form a category for lack of composability of the morphisms; one example of this problem is the class of probabilistic automata when equipped with morphisms that allow restriction as well as relabelling. The proper mathematical framework for this situation is provided by a generalisation of category theory in the shape of the so-called precategories, which are introduced and studied in this paper. In particular, notions of adjointness, weak adjointness and partial adjointness for precategories are presented and justified in detail. This makes it possible to use universal properties as characterisations of well-known basic constructions in the theory of (generative) probabilistic automata: we show that accessible automata and decision trees, respectively, form coreflective subprecategories of the precategory of probabilistic automata. Moreover, the aggregation of two automata is identified as a partial product, whereas restriction and interconnection of automata are recognised as Cartesian lifts.