A canonical cover generalizing the left Fischer cover to arbitrary sofic
shifts is introduced and used to prove that the left Krieger cover and the past
set cover of a sofic shift can be divided into natural layers. These results
are used to find the range of a flow-invariant and to investigate the ideal
structure of the universal C*-algebra associated to a sofic shift space.Comment: To appear in Documenta Mathematica. Section 2 has been shortened.
Three sections concerning the layered structure of the left Krieger cover and
the past set cover have been merged and rewritten. Non-essential examples
have been omitted. 21 pages, 8 figure
