J. Goguen. Realization is universal. Mathematical Systems Theory, 6:359{ 374, 1972. Home/Search Document Not in Database Summary Related Articles Check |
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Paracategories II: Adjunctions, fibrations and examples from.. - Hermida, Mateus (2002) (Correct)
.... Automata Theory Several results on automata theory can be elegantly explained using categorical language [AM74, AT91] since an automaton is essentially an action over a monoid [EW67] Bearing this in mind, it is easy to explain combination and realization of automata as universal constructions [Gog72, WN95]. Most of these results can be extended to richer structures, such as linear, internal and non deterministic automata [Ad a76] However, probabilistic automata tend to be an exception to this elysian setting, specially when we need to restrict the probabilistic transitions of an automata ....
J. Goguen. Realization is universal. Mathematical Systems Theory, 6:359{ 374, 1972.
Behavioural Differential Equations: A Coinductive Calculus of.. - Rutten (2000) (Correct)
....The reader is invited to consult [Gin68, pp.68 69] which contains a minor variation on the example K = L, at the end 40 of Section 10, and convince himself of the greater complexity of that approach. The connection between finality and minimality, in Section 10, can already be found in [Gog73]. There are a number of different directions in which the present work can be extended. Coinduction has been formulated here, as usual, in terms of bisimulations. In [Rut98a] a more general coinduction principle is discussed for language inclusion, in terms of simulation relations. This can be ....
J. Goguen. Realization is universal. Mathematical System Theory, 6:359--374, 1973.
Automata and Coinduction (an exercise in coalgebra) - Rutten (1998) (1 citation) (Correct)
....expressions are equal (this was illustrated by the bisimulation T used for the proof of E 1 = F 1 at the end of Section 6) The question whether this can lead to (more) efficient algorithms is yet to be addressed. The connection between finality and minimality in Section 7 can already be found in [Gog73]. Our formulation of Kleene s theorem in Section 8 and its use as a criterion for nonregularity in Section 9 may be new, though the proofs involved are of course built from well known ingredients. Classically, the minimization of an automaton is obtained by identifying all states that are ....
J. Goguen. Realization is universal. Mathematical System Theory, 6:359--374, 1973.
Bisimulations and Behaviour of Nondeterministic Automata - Calude, Calude (1999) (1 citation) (Correct)
....initial states: it leads to a solution that is unique up to an isomorphism. The equivalence relation used to collapse states satisfies a condition (called in [3] well behaveness ) which is very similar to Park s bisimulation notion for concurrent branching processes. 1 Inspired by Goguen [11, 12], Kozen [16] and Rutten # Institut fur Theoretische Physik, University of Technology Vienna, Wiedner Hauptstrae 8 10 136, A 1040 Vienna, Austria; on leave from the Department of Computer Science, The University of Auckland, Private Bag 92019, Auckland, New Zealand; email: ....
Goguen, J. Realization is universal. Mathematical Systems Theory, 6 (1973), 359-- 374.
Randomly Timed Automata - Mateus, Morais, Nunes, Pacheco.. (Correct)
....notion of randomly timed automaton should be as general as possible in order to be able to support di erent execution policies. Di erent policies are studied in [19,8] for the case of stochastic Petri nets, but their usefulness extends to randomly timed automata as well. Following the style of [16,13,5,1,15,6,2,29,26] proposed for classical automata, we adopt a categorial approach to the development of the theory of randomly timed automata. However, probabilistic structures raise some speci c problems to category theory [22,25] Fortunately, we are able to avoid working with precategories as advocated in these ....
J. Goguen. Realization is universal. Mathematical Systems Theory, 6:359-374, 1972.
Realization of Probabilistic Automata: Categorical Approach - Mateus, Sernadas, Sernadas (Correct)
....same style as presented in [WN95] We also introduce the notion of probabilistic behavior allowing us to establish adjunctions between automata and behavior. In this way, we are able to extend to the probabilistic setting the classical result about the universality of minimal and free realizations [Gog73,AT89]. In section 2 of the paper we present the category of (Moore) probabilistic automata. We go on in section 3 showing that nite products and Cartesian liftings exist. We also analyze the probabilistic meaning of aggregating independent automata. Section 4 is dedicated to showing that free ....
J. Goguen. Realization is universal. Mathematical Systems Theory, 6:359{ 374, 1973.
A Categorical Manifesto - Goguen (1991) (20 citations) Self-citation (Goguen) (Correct)
....that a composition of two such morphisms is another, and that a triple of identities satisfies the diagrams and serves as an identity for composition. These checks show that we have a category Aut of automata, and their simplicity increases our confidence in the correctness of the definitions [18]. 1.6 Types. Types are used to classify things, and according to the first dogma, they should form a category having types as objects; of course, depending on what is being classified, different categories will arise. A simple example is finite product types, which are conveniently represented ....
....j : Y Y 0 , such that the diagram X 0 b 0 Y 0 j Y b X h commutes in Set. Denote this category Beh and define B : Aut Beh by B(X; S; Y; f; g) g; f and B(h; i; j) h; j) That this is a functor helps to confirm the elegance and coherence of the previous definitions. See [18]. 2.3 Models. In the Lawvere approach to universal algebra [49] an algebra is a functor from a theory T to Set. Here, construction takes the meaning of interpretation : the abstract structure in T is interpreted (i.e. constructed) concretely in Set, i.e. these functors must preserve finite ....
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Joseph Goguen. Realization is universal. Mathematical System Theory, 6:359-- 374, 1973.
Tossing Algebraic Flowers down the Great Divide - Goguen (1999) (2 citations) Self-citation (Goguen) (Correct)
....of distributed concurrent systems depends only on local interactions. There is now a slow but steady stream of research on sheaf theory in computer science, though there is not as yet a coherent community. In the early 1970s, I formulated the minimal realization of automata as an adjoint functor [38]; this soon evolved into much more general results about the minimal realization of machines in categories, which gave a neat unification of system theory (in the sense of electrical engineering) with automaton theory [36] I consider this a major vindication of the categorical approach to ....
....over time. In 1982, Meseguer and I developed a theory of abstract machines [92] for this purpose, and proved minimal (final) and initial realization theorems for them; this theory naturally generalizes algebraic ADTs as well as classical automata. The minimal realization adjunction for automata [38] helped inspire this work, and it was also pleasant to realize that many intuitions from John Guttag s early work could be vindicated [116, 117] In collaboration with Razvan Diaconescu, Rod Burstall, and most recently especially Grant Malcolm, this work has developed into a new hidden algebra ....
Joseph Goguen. Realization is universal. Mathematical System Theory, 6:359--374, 1973.
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