Wyniki wyszukiwania - BazTech

1

Comparison of descriptions of continuous-time and teletraffic systems

Borys A., Aleksiewicz M.

Zeszyty Naukowe. Telekomunikacja i Elektronika / Uniwersytet Technologiczno-Przyrodniczy w Bydgoszczy

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2012

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z. 16

5--15

EN

In a fundamental book [5] on the so-called network calculus and research papers using this technique, as for example those cited in this paper, the notion of causal linear time-invariant teletraffic systems (networks) is used. It has been mentioned in [5] that these systems are analogous to the causal linear time-invariant systems (circuits) described by integral convolution (or convolution sum in the case of discrete ones) in classical systems theory. Note that networks considered in the network calculus are described by other type of convolution that uses the infimum operation. Moreover, the algebra used in the above technique is also different. This is the so-called min-plus (or max-plus) algebra. Therefore, it is not obvious that the teletraffic systems (networks) described by the infimum convolution fulfill the following basic properties: linearity, causality, time-invariance, associativity and commutativity of their convolution operator, known from the classical theory of systems. The objective of this paper is to prove or show in detail that the above properties hold.

PL

W znanej monografii nt. rachunku sieciowego (network calculus), napisanej przez J.-Y. Le Boudeca i P. Thirana, zostało wprowadzone pojęcie liniowych systemów teleinformatycznych niezależnych od czasu. Wskazano w niej na podobieństwa istniejące pomiędzy powyższą klasą systemów a liniowymi systemami analogowymi niezależnymi od czasu, jednakże zrobiono to w sposób dosyć pobieżny. W tym artykule podobieństwa te są przeanalizowane w sposób systematyczny, a także bez uciekania się do bardzo abstrakcyjnej teorii systemów opisywanych za pomocą algebry min-plus – jedynie przy wykorzystaniu elementarnych pojęć matematyki wyższej. Wiele przedstawionych tutaj wyprowadzeń nie było dotychczas nigdzie publikowanych, jak na przykład twierdzenie 1.

2

Associativity of Infinite Synchronized Shuffles and Team Automata

ter Beek M.H., Kleijn J.

Fundamenta Informaticae

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2009

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Vol. 91, nr 3-4

4437-461

EN

Motivated by different ways to obtain team automata from synchronizing component automata, we consider various definitions of synchronized shuffles of words. A shuffle of two words is an interleaving of their symbol occurrenceswhich preserves the original order of these occurrences within each of the two words. In a synchronized shuffle, however, also two occurrences of one symbol, each from a different word, may be identified as a single occurrence. In case at least one of the words involved is infinite, a (synchronized) shuffle can also be unfair in the sense that an infinite word may prevail fromsome point onwards even when the other word still has occurrences to contribute to the shuffle. We prove that for the synchronized shuffle operations under consideration, every (fair or unfair) synchronized shuffle can be obtained as a limit of synchronized shuffles of the finite prefixes of the words involved. In addition, it is shown that with the exception of one, all synchronized shuffle operations that we consider satisfy a natural notion of associativity, also in case of unfairness. Finally, using these results, some compositionality results for team automata are established.

3

Some necessary and sufficient conditions for parastrophic invariance of the associative law in quasigroups

Jaiyeola T. G.

Fasciculi Mathematici

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2008

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Nr 40

25-35

EN

Every quasigroup (S, ⋅) belongs to a set of 6 quasi-groups, called parastrophes denoted by (S, πi), i ∈ {1, 2, 3, 4, 5, 6}. It is shown that isotopy-isomorphy is a necessary and sufficient condition for any two distinct quasigroups (S, πi) and (S, πj), i, j ∈ {1, 2, 3, 4, 5, 6} to be parastrophic invariant relative to the associative law. In addition, a necessary and sufficient condition for any two distinct quasigroups (S, πi) and (S, πj), i, j ∈ {1, 2, 3, 4, 5, 6}. to be parastrophic invariant under the associative law is either if the πi-parastrophe of H is equivalent to the πi-parastrophe of the holomorph of the πiparastrophe of S or if the πi-parastrophe of H is equivalent to the πk-parastrophe of the πi-parastrophe of the holomorph of the πi-parastrophe of S, for a particular k ∈ {1, 2, 3, 4, 5, 6}.

4

On Associative Rational Functions

Domańska K.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2005

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Vol. 10

41--65

EN

We deal with the following problem: which rational functions of two variables are associative? We shall determine all of them provided that at least of the coefficients in question vanishes.

5

A Set-Theoretic Framework for Component Composition

Moschoyiannis S., Shields M.W.

Fundamenta Informaticae

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2004

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Vol. 59, nr 4

373--396

EN

Modern software systems become increasingly complex as they are expected to support a large variety of different functions. We need to create more software in a shorter time, and without compromising the quality of the software. In order to build such systems efficiently, a compositional approach is required. This entails some formal technique for analysis and reasoning on local component properties as well as on properties of the composite. In this paper, we present a mathematical framework for the composition of software components, at a semantic modelling level. We describe a mathematical concept of a component and identify properties that ensure its potential behaviour can be captured. Based on that, we give a formal definition of composition and examine its effect on the individual components. We argue that properties of the individual components can, under certain conditions, be preserved in the composite. The proposed framework can be used for guiding the composition of components as it advocates formal reasoning about the composite before the actual composition takes place.