An axiomatization of the theory of generalized ultrametric semilattices of linear signals

Authors:
Eleftherios Matsikoudis;Edward A. Lee
Affiliations:
University of California, Berkeley;University of California, Berkeley
Venue:
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Year:
2013

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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.