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An Axiomatization of the Theory of Generalized Ultrametric Semilattices of Linear Signals

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Fundamentals of Computation Theory (FCT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8070))

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Abstract

We consider spaces of linear signals equipped with the prefix relation and a suitably defined generalized ultrametric distance function. We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and prove a representation theorem stating that generalized ultrametric semilattices with totally ordered distance sets are isomorphic to such spaces of linear signals. It follows that the definition of generalized ultrametric semilattices with totally ordered distance sets captures all formal properties of such spaces.

This work was supported in part by the Center for Hybrid and Embedded Software Systems (CHESS) at UC Berkeley, which receives support from the National Science Foundation (NSF awards #0720882 (CSR-EHS: PRET), #0931843 (CPS: Large: ActionWebs), and #1035672 (CPS: Medium: Ptides)), the Naval Research Laboratory (NRL #N0013-12-1-G015), and the following companies: Bosch, National Instruments, and Toyota.

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Authors and Affiliations

  1. University of California, Berkeley, USA

    Eleftherios Matsikoudis & Edward A. Lee

Authors
  1. Eleftherios Matsikoudis
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  2. Edward A. Lee
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Editor information

Editors and Affiliations

  1. Computer Science, University of Liverpool, Ashton Street, L69 3BX, Liverpool, UK

    Leszek Gąsieniec

  2. Department of Computer Science, University of Liverpool, United Kingdom

    Frank Wolter

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Matsikoudis, E., Lee, E.A. (2013). An Axiomatization of the Theory of Generalized Ultrametric Semilattices of Linear Signals. In: Gąsieniec, L., Wolter, F. (eds) Fundamentals of Computation Theory. FCT 2013. Lecture Notes in Computer Science, vol 8070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40164-0_24

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  • DOI: https://doi.org/10.1007/978-3-642-40164-0_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40163-3

  • Online ISBN: 978-3-642-40164-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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