Abstract
We consider a transitive sofic shift T and a SFT cover f:S→T. We define the multiplicity of the cover(S,f) to be the largest number of preimages of a point. The intrinsic multiplicity ofT is the minimum of the multiplicities over all covers of T, denoted by m(T). Is m(T) computable? We do not answer this question. However the attempt to solve this problem led us to find sharp estimates for the intrinsic multiplicity, sharpen a result of Williams, and solve a problem posed by Trow.
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