Abstract
The paper deals with the problem of liveness of weighted conservative circuits. The weight of a marking gives us an important information about its liveness. Some weights correspond only to live markings, some only to dead ones and some to both. The simultaneous presence of live and dead markings with the same weight is associated with the presence of several equivalence classes generated by the solutions of the state equation. We call such classes orbits. It is impossible to reach from a given marking a state belonging to a different orbit and this creates an opportunity of coexistence of a dead and a live marking with the same weight. Different orbits are also associated with the presence of a kind of frozen tokens, which we call half frozen. A discussion of problems associated with deter-mining liveness for weighted circuits follows and an arithmetical condition to determine whether a given marking is live is presented.
This work has been supported by the ESPRIT Basic Research Project CALIBAN, WG 6067
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References
Brauer A. On a problem of partitions, Amer.J.Math. 1942; 64: 299–312
Chrząstowski-Wachtel P, Raczunas M. Liveness of Weighted Circuits and the Diophantine problem of Frobenius. Proceedings from the Workshop on Concurrency, Specification and Programming, November 19–21, 1992, Berlin; Fachbereich Informatik der Humboldt-Univeritaet zu Berlin 1993, Informatik-Preprint 22
ChrzÄ…stowski-Wachtel P, Raczunas M. Liveness of Weighted Circuits and the Diophantine problem of Frobenius. Proceedings from the Fundamentals of Computation Theory conference, Szeged 1993, LNCS 710
Raczunas M, ChrzÄ…stowski-Wachtel P. A Diophantine problem of Frobenius in terms of the least common multiple. To appear in Discrete Mathematics
Selmer ES. On the linear Diophantine problem of Frobenius J. reine angew. Math. 1977; 293 /294: 1–17
Teruel E, Chrząstowski-Wachtel P, Colom JM, Silva M. On weighted T-systems. Advances in Petri Nets, Lecture Notes in Computer Science, 1992; vol. 616: 348–367
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© 1995 British Computer Society
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Chrz̧stowski-Wachtel, P., Raczunas, M. (1995). Orbits, half-frozen tokens and the liveness of weighted circuits. In: Desel, J. (eds) Structures in Concurrency Theory. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3078-9_8
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DOI: https://doi.org/10.1007/978-1-4471-3078-9_8
Publisher Name: Springer, London
Print ISBN: 978-3-540-19982-3
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