Theoretical Computer Science - Conference on arithmetics and coding systems, Marseille-Luminy, June 1987
IEEE Transactions on Information Theory
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Consider a sofic dynamical system (X, T, μ), where X =A Z is the full symbolic compact set with the product topology, and A = {0, 1, . . . , d}. The shift is $$ T:\left\{ {{x_n}} \right\}\to \left\{ {{{{x^{\prime}}}_n}} \right\},{{x^{\prime}}_n}={x_n}+1 $$ . The measure μ is a T-invariant sofic probability measure. For all words a 1 . . . a n the measure is μ(a 1 . . . a n ) = μ({x : x 1 = a 1, . . . , x n = a n }) = $$ l{m_{{{a_1}}}}\ldots {m_{{{a_n}}}}r $$ . Matrices {m 0, . . . , m d }, d 驴 1, are nonzero substochastic matrices of order J. The matrix P = m 0 +. . . + m d is a stochastic matrix, the row l is a left P-invariant probability row and all entries of the column r are equal to 1.We obtain an explicit formula for the entropy h(T, μ) of sofic dynamical system of Blackwell's type for which rank(m a ) = 1, a 驴 0.