caa a22 4500 445378646 CHVBK 20180317143010.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10485-010-9233-0 doi (NATIONALLICENCE)springer-10.1007/s10485-010-9233-0 The Compositional Construction of Markov Processes [Elektronische Daten] [Luisa de Francesco Albasini, Nicoletta Sabadini, Robert Walters] We describe a symmetric monoidal category whose arrows are automata in which the actions have probabilities. The endomorphisms of the identity for the tensor are classical finite Markov processes. The operations of the category permit the compositional description Markov processes. We illustrate by describing a Markov process with 12n states, which represents a model of the classical Dining Philosopher problem with n dining philosophers, showing how to calculate the probability of reaching deadlock in k steps. A straightforward application of the Perron-Frobenius Theorem yields that this probability tends to 1 as k tends to infinity. Springer Science+Business Media B.V., 2010 Probabilistic automaton nationallicence Symmetric monoidal category nationallicence Compact closed nationallicence Markov process nationallicence Frobenius algebra nationallicence Compositionality nationallicence de Francesco Albasini Luisa Dipartimento di Fisica e Matematica, Università Degli Studi Dell'Insubria, via Carloni 78, 22100, Como, CO, Italy aut Sabadini Nicoletta Dipartimento di Informatica e Comunicazione, Università degli Studi dell'Insubria, via Carloni 78, 22100, Como, CO, Italy aut Walters Robert Dipartimento di Informatica e Comunicazione, Università degli Studi dell'Insubria, via Carloni 78, 22100, Como, CO, Italy aut Applied Categorical Structures Springer Netherlands 19/1(2011-02-01), 425-437 0927-2852 19:1<425 2011 19 10485 https://doi.org/10.1007/s10485-010-9233-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-010-9233-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- de Francesco Albasini Luisa Dipartimento di Fisica e Matematica, Università Degli Studi Dell'Insubria, via Carloni 78, 22100, Como, CO, Italy aut NATIONALLICENCE 700 1- Sabadini Nicoletta Dipartimento di Informatica e Comunicazione, Università degli Studi dell'Insubria, via Carloni 78, 22100, Como, CO, Italy aut NATIONALLICENCE 700 1- Walters Robert Dipartimento di Informatica e Comunicazione, Università degli Studi dell'Insubria, via Carloni 78, 22100, Como, CO, Italy aut NATIONALLICENCE 773 0- Applied Categorical Structures Springer Netherlands 19/1(2011-02-01), 425-437 0927-2852 19:1<425 2011 19 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer