Citation
Eleftherios Matsikoudis, Edward A. Lee. "The fixed-point theory of strictly causal functions". Theoretical Computer Science, 574:39-77, April 2015.

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 modeling 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, introduce a corresponding induction principle, and study the related convergence process.

Electronic downloads

• http://dx.doi.org/10.1016/j.tcs.2015.01.036

• HTML

  Eleftherios Matsikoudis, Edward A. Lee. <a
  href="http://chess.eecs.berkeley.edu/pubs/1113.html"
  >The fixed-point theory of strictly causal
  functions</a>, <i>Theoretical Computer
  Science</i>, 574:39-77, April 2015.

• Plain text

  Eleftherios Matsikoudis, Edward A. Lee. "The
  fixed-point theory of strictly causal functions".
  <i>Theoretical Computer Science</i>, 574:39-77,
  April 2015.

• BibTeX

  @article{MatsikoudisLee15_FixedpointTheoryOfStrictlyCausalFunctions,
      author = {Eleftherios Matsikoudis and Edward A. Lee},
      title = {The fixed-point theory of strictly causal functions},
      journal = {Theoretical Computer Science},
      volume = {574},
      pages = {39-77},
      month = {April},
      year = {2015},
      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 modeling 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, introduce a corresponding induction
                principle, and study the related convergence
                process.},
      URL = {http://chess.eecs.berkeley.edu/pubs/1113.html}
  }
  

Posted by Mary Stewart on 15 Sep 2015.
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