Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Generalized Ultrametric Semilattices of Linear Signals

Eleftherios Matsikoudis and Edward A. Lee

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2014-7
January 23, 2014

http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-7.pdf

We consider certain spaces of linear signals equipped with a standard prefix relation and a suitably defined generalized distance function. We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and prove a representation theorem stating that every generalized ultrametric semilattice with a totally ordered distance set is isomorphic to a space of that kind. It follows that the formal definition of generalized ultrametric semilattices with totally ordered distance sets constitutes an axiomatization of the first-order theory of those spaces.


BibTeX citation:

@techreport{Matsikoudis:EECS-2014-7,
    Author = {Matsikoudis, Eleftherios and Lee, Edward A.},
    Title = {Generalized Ultrametric Semilattices of Linear Signals},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2014},
    Month = {Jan},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-7.html},
    Number = {UCB/EECS-2014-7},
    Abstract = {We consider certain spaces of linear signals equipped with a standard prefix relation and a suitably defined generalized distance function. We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and prove a representation theorem stating that every generalized ultrametric semilattice with a totally ordered distance set is isomorphic to a space of that kind. It follows that the formal definition of generalized ultrametric semilattices with totally ordered distance sets constitutes an axiomatization of the first-order theory of those spaces.}
}

EndNote citation:

%0 Report
%A Matsikoudis, Eleftherios
%A Lee, Edward A.
%T Generalized Ultrametric Semilattices of Linear Signals
%I EECS Department, University of California, Berkeley
%D 2014
%8 January 23
%@ UCB/EECS-2014-7
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-7.html
%F Matsikoudis:EECS-2014-7