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PSEUDOVARIETIES DEFINING CLASSES OF SOFIC SUBSHIFTS CLOSED FOR TAKING SHIFT EQUIVALENT

By Alfredo Manuel Gouveia Da Costa

Abstract

For a pseudovariety V of ordered semigroups, let S (V) be the class of sofic subshifts whose syntactic semigroup lies in V. It is proved that if V contains Sl − then S (V∗D) is closed for taking shift equivalent subshifts, and conversely, if S (V) is closed for taking conjugate subshifts then V contains LSl − and S (V) = S (V∗D). Almost finite type subshifts are characterized as the irreducible elements of S (LInv), which gives a new proof that the class of almost finite type subshifts is closed for taking shift equivalent subshifts

Topics: pseudovariety, subshift, sofic, conjugacy, shift equivalence
Year: 2005
OAI identifier: oai:CiteSeerX.psu:10.1.1.135.1065
Provided by: CiteSeerX
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