Multiplicities of covers for sofic shifts

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...

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Veröffentlicht in:	Theoretical computer science 2001-07, Vol.262 (1-2), p.349-375
Hauptverfasser:	Fiebig, Doris, Fiebig, Ulf-Rainer, Jonoska, Nataša
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithmics. Computability. Computer arithmetics Applied sciences Combinatorics Combinatorics. Ordered structures Computer science control theory systems Exact sciences and technology Graph theory Mathematics Sciences and techniques of general use Theoretical computing
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Zusammenfassung:	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.
ISSN:	0304-3975 1879-2294
DOI:	10.1016/S0304-3975(00)00278-4