Abstract
It is shown that two deterministic gsm replicationsτ 1 andτ 2 are equivalent on the supportL of aQ-rational formal power series if and only ifτ 1 (w) = τ2 (w) for allw inL such that the length ofw does not exceed a certain bound which depends only on the numbers of states in the deterministic gsm's involved and on the size of the matrix system acceptingL. Application of this result to the deterministic gsm equivalence problem improves known bounds. Finally, sufficient conditions for an arbitrary family of languages to have a decidable deterministic gsm replication equivalence problem are presented.
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Turakainen, P. The equivalence of deterministic gsm replications onQ-rational languages is decidable. Math. Systems Theory 20, 273–282 (1987). https://doi.org/10.1007/BF01692070
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DOI: https://doi.org/10.1007/BF01692070