Lifting covers of sofic shifts
by
Paul Trow
The University of Memphis

We define a class of factor maps between sofic shifts, called "lifting maps", which generalize the closing maps. We show that every left (or right) lifting cover of a sofic shift is conjugate to a left (or right) determining cover. This generalizes the fact that a left closing cover is conjugate to a left resolving cover. We also show that every sofic shift has a finite collection of minimal left (or right) lifting covers; consequently, every left (or right) lifting cover factors through one in the finite collection. This generalizes the fact that every left closing cover factors through the left Fischer cover. The collection of minimal closing covers forms a conjugacy invariant for the sofic shift.

Date received: March 15, 1998