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We apply a theory of infinite labeled graphs to studying presentations and classifications of symbolic dynamical systems, by introducing a class of infinite labeled graphs, called λ-graph systems. Its matrix presentation is called a symbolic matrix system. The notions of a λ-graph system and symbolic matrix system are generalized notions of a finite labeled graph and symbolic matrix for sofic subshifts...
We generalize the Bowen–Franks groups for topological Markov shifts to general subshifts as the Ext-groups for the associated C*-algebras. The generalized Bowen–Franks groups for subshifts are shown to be invariant under flow equivalence and, hence, invariant under topological conjugacy. They are regarded as the indices of Fredholm operators related to extensions of the associated C*-algebras so...
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