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On Fixed Points of Strictly Causal Functions

  • Conference paper
Formal Modeling and Analysis of Timed Systems (FORMATS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8053))

Abstract

We ask whether strictly causal components form well defined systems when arranged in feedback configurations. The standard interpretation for such configurations induces a fixed-point constraint on the function modelling the component involved. We define strictly causal functions formally, and show that the corresponding fixed-point problem does not always have a well defined solution. We examine the relationship between these functions and the functions that are strictly contracting with respect to a generalized distance function on signals, and argue that these strictly contracting functions are actually the functions that one ought to be interested in. We prove a constructive fixed-point theorem for these functions, and introduce a corresponding induction principle.

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. Facultad de Ciencias Exactas y Naturales, Departamento de Computación, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, Intendente Güiraldes 2160, C1428EGA, Buenos Aires, Argentina

    Víctor Braberman

  2. LSV, CNRS & ENS de Cachan, 61, avenue du Président Wilson, 94235, Cachan Cedex, France

    Laurent Fribourg

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Matsikoudis, E., Lee, E.A. (2013). On Fixed Points of Strictly Causal Functions. In: Braberman, V., Fribourg, L. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2013. Lecture Notes in Computer Science, vol 8053. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40229-6_13

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  • DOI: https://doi.org/10.1007/978-3-642-40229-6_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40228-9

  • Online ISBN: 978-3-642-40229-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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