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Liveness of weighted circuits and the diophantine problem of Frobenius

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Book cover Fundamentals of Computation Theory (FCT 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 710))

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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. The diophantine problem of Frobenius is used to determine a formula for the least live weight.

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References

  1. A. Brauer. On a problem of partitions. Amer.J.Math., 64 (1942)

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  2. P. Chrzastowski-Wachtel, M. Raczunas. Liveness of Weighted Circuits and the diophantine problem of Frobenius Technical Report, Humboldt University, Berlin 1993

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  3. M. Raczunas, P. Chrzastowski-Wachtel. A diophantine problem of Frobenius in terms of the least common multiple submitted to Acta Arithmetica

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  4. E. S. Selmer. On the linear diophantine problem of Frobenius J.reine angew. Math. 293/294 (1977)

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  5. E. Teruel, P. Chrzastowski-Wachtel, J. M. Colom, M. Silva. On weighted T-systems. Advances in Petri Nets, Lecture Notes in Computer Science, vol.616, Springer Verlag (1992)

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Authors and Affiliations

  1. Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097, Warszawa, Poland

    Piotr Chrzastowski-Wachtel

  2. Institute of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, 80-952, Gdańsk, Poland

    Marek Raczunas

Authors
  1. Piotr Chrzastowski-Wachtel
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  2. Marek Raczunas
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Zoltán Ésik

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© 1993 Springer-Verlag Berlin Heidelberg

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Chrzastowski-Wachtel, P., Raczunas, M. (1993). Liveness of weighted circuits and the diophantine problem of Frobenius. In: Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 1993. Lecture Notes in Computer Science, vol 710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57163-9_13

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  • DOI: https://doi.org/10.1007/3-540-57163-9_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57163-6

  • Online ISBN: 978-3-540-47923-9

  • eBook Packages: Springer Book Archive

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