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INTERCONNECTION OF PROBABILISTIC SYSTEMS
, 2000
"... There is a growing interest in models for probabilistic systems. This fact is motivated by engineering applications, namely in problems concerning the evaluation of the performance of systems. It is of ..."
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There is a growing interest in models for probabilistic systems. This fact is motivated by engineering applications, namely in problems concerning the evaluation of the performance of systems. It is of
Monads on Composition Graphs
 UNIVERSITY OF BREMEN
, 2000
"... Collections of objects and morphisms that fail to form categories inasmuch as the expected composites of two morphisms need not always be defined have been introduced in [14, 15] under the name composition graphs. In [14, 16], notions of adjunction and weak adjunction for composition graphs have bee ..."
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Collections of objects and morphisms that fail to form categories inasmuch as the expected composites of two morphisms need not always be defined have been introduced in [14, 15] under the name composition graphs. In [14, 16], notions of adjunction and weak adjunction for composition graphs have been proposed. Building on these definitions, we now introduce a concept of monads for composition graphs and show that the usual correspondence between adjunctions and monads remains correct, i.e. that (weak) adjunctions give rise to monads and that all monads are induced by adjunctions. Monads are described in terms of natural transforms as well as in terms of Kleisli triples, which seem to be better suited in the absence of associativity. The realization of a monad by an adjunction relies on a generalization of the Kleisli construction to composition graphs; on the other hand, the EilenbergMoore construction produces only a weak adjunction and admits comparison functors from weak adjuncti...
MODELLING MULTIAGENT INTERACTION PROTOCOLS USING CATEGORIES ENRICHED OVER POINTED SETS
"... Abstract. The study of multiagent systems is proving to be an exciting and active research field within computer science. Communication is an important aspect of multiagent systems, and the protocols that are used to provide a shared definition of what agents can say to each other, along with the ..."
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Abstract. The study of multiagent systems is proving to be an exciting and active research field within computer science. Communication is an important aspect of multiagent systems, and the protocols that are used to provide a shared definition of what agents can say to each other, along with the meaning of what agents say, receive much attention from researchers. At present, there are a number of welldefined protocols, agent communication languages, and protocol specification languages available, yet, there is no formal mathematical theory of agent interaction protocols. The authors believe that such a theory would be beneficial to the field of agent communication and multiagent systems in general. In this paper, we present an application of the mature field
Realization of Probabilistic Automata: Categorical Approach
 Recent Developments in Algebraic Development Techniques  Selected Papers, volume 1827 of Lecture Notes in Computer Science. SpringerVerlag. In print
"... . 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 ..."
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. 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...
Paracategories II: Adjunctions, fibrations and examples from probabilistic automata theory
, 2002
"... In this sequel to [HM02], we explore some of the global aspects of the category of paracategories. We establish its (co)completeness and cartesian closure. From the closed structure we derive the relevant notion of transformation for paracategories. We setup the relevant notion of adjunction betwee ..."
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In this sequel to [HM02], we explore some of the global aspects of the category of paracategories. We establish its (co)completeness and cartesian closure. From the closed structure we derive the relevant notion of transformation for paracategories. We setup the relevant notion of adjunction between paracategories and apply it to define (co)completeness and cartesian closure, exemplified by the paracategory of bivariant functors and dinatural transformations. We introduce partial multicategories to account for partial tensor products. We also consider fibrations for paracategories and their indexedparacategory version. Finally, we instantiate all these concepts in the context of probabilistic automata.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1 Optimal Supervisory Control of Probabilistic Discrete Event Systems
"... Abstract—Probabilistic discrete event systems (PDES) are modeled as generators of probabilistic languages and the supervisors employed are a probabilistic generalization of deterministic supervisors used in standard supervisory control theory. In the case when there exists no probabilistic superviso ..."
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Abstract—Probabilistic discrete event systems (PDES) are modeled as generators of probabilistic languages and the supervisors employed are a probabilistic generalization of deterministic supervisors used in standard supervisory control theory. In the case when there exists no probabilistic supervisor such that the behaviour of a plant under control exactly matches the probabilistic language given as the requirements specification, we want to find a probabilistic control such that the behaviour of the plant under control is “as close as possible ” to the desired behaviour. First, as a measure of this proximity, a pseudometric on states of generators is defined. Two algorithms for the calculation of the distance between states in this pseudometric are described. Then, an algorithm to synthesize a probabilistic supervisor that minimizes the distance between generators representing the achievable and required behaviour of the plant is presented. I.