Book ChapterDOI
Idempotency: Algebraic system analysis of timed Petri nets
TLDR
It is shown that Continuous Timed Petri Nets (CTPN) can be modeled by generalized polynomial recurrent equations in the (min,+) semiring and a correspondence between CTPN and Markov decision processes is established.Abstract:
We show that Continuous Timed Petri Nets (CTPN) can be modeled by generalized polynomial recurrent equations in the (min,+) semiring. We establish a correspondence between CTPN and Markov decision processes. We survey the basic system theoretical results available: behavioral (inputoutput) properties, algebraic representations, asymptotic regime. A particular attention is paid to the subclass of stable systems (with asymptotic linear growth).read more
Citations
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Journal ArticleDOI
On Hybrid Petri Nets
René David,Hassane Alla +1 more
TL;DR: This paper is a survey of the work of the authors' team on hybridPNs (definition, properties, modeling), and contains new material such as the definition of extended hybrid PNs and several applications, explanations and comments about the timings in Petri nets, more on the conflict resolution in Hybrid PNs, and connection between hybrid PN and hybrid automata.
Journal ArticleDOI
Max-plus algebra and system theory: Where we are and where to go now
TL;DR: More than sixteen years after the beginning of a linear theory for certain discrete event systems in which max-plus algebra and similar algebraic tools play a central role, this article summarized some of the main achievements in an informal style based on examples.
Journal ArticleDOI
Modeling and analysis of timed Petri nets using heaps of pieces
Stéphane Gaubert,Jean Mairesse +1 more
TL;DR: It is shown that safe timed Petri nets can be represented by special automata over the (max,+) semiring, which compute the height of heaps of pieces, and a heap-based throughput formula is obtained, which is simpler to compute than its traditional timed event graph version.
Journal ArticleDOI
Fuzzy h-ideals of hemirings
Jianming Zhan,WiesBaw A. Dudek +1 more
TL;DR: It is proved that a fuzzy subset @z of a hemiring S is a prime fuzzy left (right) h-ideal of S if and only if @z is two-valued, @z(0)=1, and the set of all x in S such that @z
Journal ArticleDOI
On fluidization of discrete event models: observation and control of continuous Petri nets
TL;DR: This work provides a broad tutorial on the fluidization of discrete event dynamic models, an efficient technique for dealing with the classical state explosion problem and the use of structure theory of (discrete) PNs, algebraic and graph based concepts and results; and the bridge to Automatic Control Theory.
References
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Book
A Compendium of Continuous Lattices
TL;DR: In this article, the authors present a primer of complete lattices and complete topology of continuous lattices, including the Scott topology and meet-continuous lattices.
Book
Rational Series and Their Languages
TL;DR: This chapter discusses the development of Rational Series over a Principal Ring, a model based on the model developed in Chapter I, and its applications to Languages and Codes.
Journal ArticleDOI
Algebraic tools for the performance evaluation of discrete event systems
TL;DR: In this article, it was shown that a certain class of Petri nets called event graphs can be represented as linear time-invariant finite-dimensional systems using some particular algebras.
Book
Graphes et algorithmes
Michel Gondran,Michel Minoux +1 more
TL;DR: Les algorithmes approches / Annexes :Programmation lineaire - Programmation LINEAIR en nombres entiers - Relaxation lagrangienne et resolution du probleme dual - Programme dynamique - Les problemes de ratio m minimumm as discussed by the authors.