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to be exhaustive. On the algebraic side, we did not discuss such issues as “lineardependence” in “vector spaces” on dioids (sets D n with an internal addition ⊕and an external multiplication ⊗ by scalars in D). This issue is basic for thesystem-theoretic issue of “minimal realizations”, a question which is still open(see however [14]). There are several possible definitions of linear dependence[13] and one of them can be characterized by the condition of some “determinant”being null [9]. We did not either discuss the Cayley-Hamilton theorem(see [12, 16]): it holds true in dioids simply because of the proof of Straubing[18] which is based only on combinatorial properties that are common to boththe conventional and the dioid algebras. However, the formulation of Cayley-Hamilton theorem in dioids requires some care because of the lack of “minussign” in these algebras. This theorem should play an important role in realizationtheory.On the system-theoretic side, apart from the basic question of minimal realization,we believe that control and optimization issues should be more developpedfor this theory to prove practically useful. In this paper, we did notreview such notions as “stability” and structural controllability and observabilitypreviously introduced in the framework of dater equations, nor the associatedresults concerning stabilizability by dynamic output feedback [4]. The practicalsignificance of these results in the framework of flexible manufacturing systemswas discussed in earlier papers [2, 3].Anyway, considering the amount of efforts that has been devoted to thedevelopment of conventional linear system theory during at least twenty years,it must be considered that this new sytem theory is just in its infancy. However,it is interesting to see how continuous systems and discrete event systems canbe essentially considered from the same points of view and concepts, providedthat the algebra be adapted. This requires a specific effort.Acknowledgement Mr. Ramine Nikoukhah who recently joined our group(on leave from MIT) helped us in clarifying some points such as the issue ofinitial conditions. His contribution is gratefully acknowledged.References[1] P. Caspi and N. Halbwachs, “A functional model for describing and reasoningabout time behaviour of computing systems ”, Acta Informatica, Vol.22, pp. 595–627, 1986.[2] G. Cohen, D. Dubois, J.P. Quadrat and M. Viot, “Analyse du comportementpériodique des systèmes de production par la théorie des dioides”,INRIA Report No. 191, Le Chesnay, France, 1983.[3] G. Cohen, D. Dubois, J.P. Quadrat and M. Viot, “A linear system theoreticview of discrete event processes and its use for performance evaluation in46