Citation
Eleftherios Matsikoudis, Edward A. Lee. "The Fixed-Point Theory of Strictly Contracting Functions on Generalized Ultrametric Semilattices". Workshop on Fixed Points in Computer Science (FICS), Torino, Italy, 1, September, 2013.

Abstract
We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and in which the meet operation of the semilattice coexists with a generalized distance function in a tightly coordinated way. We prove a constructive fixed-point theorem for strictly contracting functions on directed complete generalized ultrametric semilattices, and introduce a corresponding induction principle. We cite examples of application in the semantics of logic programming and timed computation, where, until now, the only tool available has been the non-constructive fixed-point theorem of Priess-Crampe and Ribenboim for strictly contracting functions on spherically complete generalized ultrametric spaces.

Electronic downloads

• http://dx.doi.org/10.4204/EPTCS.126.5

• HTML

  Eleftherios Matsikoudis, Edward A. Lee. <a
  href="http://chess.eecs.berkeley.edu/pubs/1014.html"
  >The Fixed-Point Theory of Strictly Contracting Functions
  on Generalized Ultrametric Semilattices</a>, Workshop
  on Fixed Points in Computer Science (FICS), Torino, Italy,
  1, September, 2013.

• Plain text

  Eleftherios Matsikoudis, Edward A. Lee. "The
  Fixed-Point Theory of Strictly Contracting Functions on
  Generalized Ultrametric Semilattices". Workshop on
  Fixed Points in Computer Science (FICS), Torino, Italy, 1,
  September, 2013.

• BibTeX

  @inproceedings{MatsikoudisLee13_FixedPointTheoryOfStrictlyContractingFunctionsOnGeneralized,
      author = {Eleftherios Matsikoudis and Edward A. Lee},
      title = {The Fixed-Point Theory of Strictly Contracting
                Functions on Generalized Ultrametric Semilattices},
      booktitle = {Workshop on Fixed Points in Computer Science
                (FICS), Torino, Italy},
      day = {1},
      month = {September},
      year = {2013},
      abstract = {We introduce a new class of abstract structures,
                which we call generalized ultrametric
                semilattices, and in which the meet operation of
                the semilattice coexists with a generalized
                distance function in a tightly coordinated way. We
                prove a constructive fixed-point theorem for
                strictly contracting functions on directed
                complete generalized ultrametric semilattices, and
                introduce a corresponding induction principle. We
                cite examples of application in the semantics of
                logic programming and timed computation, where,
                until now, the only tool available has been the
                non-constructive fixed-point theorem of
                Priess-Crampe and Ribenboim for strictly
                contracting functions on spherically complete
                generalized ultrametric spaces.},
      URL = {http://chess.eecs.berkeley.edu/pubs/1014.html}
  }
  

Posted by Eleftherios Matsikoudis on 5 Sep 2013.
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