Multiplicities of SFT covers
by
Natasha Jonoska
University of South Florida
Coauthors: Doris Fiebig, Ulf Fiebig

We introduce the notion of multiplicity of a sofic shift S as the least number of the maximal number of preimages in SFT covers of S. We show that there are sofic shifts such that no cover of least multiplicity is a factor of the fiber product of the left and the right Fischer covers. An example of a sofic shift such that every cover of minimal multiplicity has more vertices than the left or the right Fischer covers is presented. We reconstruct the example of S. Williams and we show that there is a sofic shift with infinite number of minimal covers with minimal multiplicity.

Date received: March 10, 1998