Abstract
In this paper, we introduce a particular model of massively parallel net, made of the connexions of identical patterns. As a matter of fact, one can construct in a modular way an infinite family of nets from a given pattern. In this framework, we raise an entirely original class of problems : prove that, for any such net, whatever the execution is, some properties are verified and some other are not. The originality (and the difficulty) comes from the fact that the family of nets is infinite. We give a method for validating a pattern with respect to the deadlock problem. If a pattern is valid, then any net, constructed by connecting an arbitrary number of patterns in an arbitrary way, is deadlock-free.
This work has been supported by the P.R.C. C3, Ministère de la Recherche et de la Technologie.
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Beauquier J, Choquet A., Petit A., Vidal-Naquet G.,Syntactic properties of unbounded nets of processors, CAAP 1989, Lecture Notes in Computer Science 351, Barcelone, 1989.
Beauquier J, Choquet A., Petit A., Vidal-Naquet G.,Detection of deadlocks in an infinite family of nets, Technical report no 594, Université Paris-Sud, France, 1990.
Berstel J.,Transductions and context-free languages, Teubner, Stuttgart, 1979.
Borkar S., Cohn R., Cox G., Gross T., Kung H. T., Lam M., Levine M., Moore B., Moore W., Peterson C., Susman J., Sutton J., Urbanski J., Webb J.,Supporting Systolic and Memory Communication in iWarp, Proceedings of the 17th Inter. Symp. on Computer Architecture, pp 70–81, 1990.
Brookes, Roscoe,Deadlock analysis in networks of communicating process, Logic and Models of Concurrent Systems (K.R. Apt ed.), NATO ASI series F, Vol 13, Springer, 1985.
Ginsburg S.,The Mathematical Theory of Context-Free Languages, McGraw-Hill, New-York, 1966.
Hillis W.D.,The Connection Machine, MIT Press, 1985.
Kohonen T.,An introduction to neural computing, Neural Networks, vol 1, pp 3–16, 1988.
Lambert J.-L.,Le problème de l'accessibilité dans les réseaux de Petri, Thèse, Université de Paris-Sud, 1987.
Parikh R.J., On context free languages, Journal Assoc. Comp. Mach. 13, pp 570–581, 1966.
Quinton P., An introduction to systolic architectures, Future Parallel Computer, LNCS 272, pp387–400, 1986.
Romeuf J.-F.,A polynomial algorithm for solving systems of two linear diophantine equations, Theoretical Computer Science 74, pp 329–340, 1990.
van Tillborg A.M.,Panel on Future Directions in Parallel Computer Architecture, Computer Architecture News, pp 3–53, 1989.
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© 1991 Springer-Verlag Berlin Heidelberg
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Beauquier, J., Choquet, A., Petit, A., Vidal-Naquet, G. (1991). Detection of deadlocks in an infinite family of nets. In: Choffrut, C., Jantzen, M. (eds) STACS 91. STACS 1991. Lecture Notes in Computer Science, vol 480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020810
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DOI: https://doi.org/10.1007/BFb0020810
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