Quantification du taux d’invalidité d’applications temps-réel à contraintes strictes

Largeteau, Gaëlle; Geniet, Dominique

doi:10.3166/tsi.27.589-625

Cited by 6 publications

(5 citation statements)

References 8 publications

(8 reference statements)

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“…The first values were found in 1972 up to n = 6 [17] and the last one (to our knowledge) in 2006, up to n = 18 [2]. If we extend the notion of polycube to d-dimensions, where d 3, these objects are also used in an efficient model of real-time validation [16], as well as in the representation of finite geometrical languages [8,14,12].…”

Section: Introductionmentioning

confidence: 90%

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Enumeration of Specific Classes of Polycubes

Champarnaud¹,

Cohen-Solal²,

Dubernard³

et al. 2013

Electron. J. Combin.

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The aim of this paper is to gather several results concerning the enumeration of specific classes of polycubes. We first consider two classes of $3$-dimensional vertically-convex directed polycubes: the plateau polycubes and the parallelogram polycubes. An expression of the generating function is provided for the former class, as well as an asymptotic result for the number of polycubes of each class with respect to volume and width. We also consider three classes of $d$-dimensional polycubes $(d\geq 3)$ and we state asymptotic results for the number of polycubes of each class with respect to volume and width.

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Section: Introductionmentioning

confidence: 90%

“…polycubes with respect to the above-mentioned parameters. Let us notice that these polycubes appear in the modelling of real-time applications composed of two periodic tasks [15].…”

Section: Some Propositions About Parallelogram Polycubesmentioning

confidence: 99%

Enumeration of Specific Classes of Polycubes

Champarnaud¹,

Cohen-Solal²,

Dubernard³

et al. 2013

Electron. J. Combin.

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show abstract

“…The first values were found in 1972 up to n = 6 [17] and the last one (to our knowledge) in 2006, up to n = 18 [4]. The notion of polycube can be extended to dimension d, with d ≥ 3; d-dimensional polycubes (or d-polycubes for short) are used in an efficient model of real-time validation [16], as well as in the representation of finite geometrical languages [5,12]. Although the polycubes are higher dimensional natural analogues of polyominoes, very little is known about their enumeration.…”

Section: Introductionmentioning

confidence: 93%

Dirichlet convolution and enumeration of pyramid polycubes

Carré,

Debroux,

Deneufchatel

et al. 2013

Preprint

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“…Polyhypercubes are also called d-polycubes. They are used in an efficient model for real time validation [12] and in representation of finite geometric languages [8]. There is no explicit formula for A d (n) the number of polyhypercubes in dimension d with n cells.…”

Section: Introductionmentioning

confidence: 99%