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The Structure of the One-Generated Free Domain Semiring

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Relations and Kleene Algebra in Computer Science (RelMiCS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4988))

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Abstract

This note gives an explicit construction of the one-generated free domain semiring. In particular it is proved that the elements can be represented uniquely by finite antichains in the poset of finite strictly decreasing sequences of nonnegative integers. It is also shown that this domain semiring can be represented by sets of binary relations with union, composition and relational domain as operations.

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References

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Author information

Authors and Affiliations

  1. Chapman University, One University Dr, Orange, CA 92866, USA

    Peter Jipsen

  2. The University of Sheffield, 211 Portobello Street, Sheffield, S1 4DP, UK

    Georg Struth

Authors
  1. Peter Jipsen
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  2. Georg Struth
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Rudolf Berghammer Bernhard Möller Georg Struth

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© 2008 Springer-Verlag Berlin Heidelberg

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Jipsen, P., Struth, G. (2008). The Structure of the One-Generated Free Domain Semiring. In: Berghammer, R., Möller, B., Struth, G. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2008. Lecture Notes in Computer Science, vol 4988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78913-0_18

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  • DOI: https://doi.org/10.1007/978-3-540-78913-0_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78912-3

  • Online ISBN: 978-3-540-78913-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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