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Journal of Automata, Languages and Combinatorics
formerly:
Journal of Information Processing and Cybernetics /
Elektronische Informationsverarbeitung und Kybernetik
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@article{jalc040102,
author = {Ion Petre},
title = {Parikh's Theorem Does Not Hold for Multiplicities},
journal = jalc,
year = 1999,
volume = 4,
number = 1,
pages = {17--30},
keywords = {Parikh's Theorem, multiplicities, formal power series,
Mezei's Theorem},
abstract = {We consider the question of whether the famous Parikh's
Theorem holds with multiplicities i.e., for formal power
series instead of languages. The strict hierarchy of
algebraic, rational, recognizable and semilinear formal
power series in commuting variables is proved and in this
way it is established that the Parikh's Theorem does not
hold with multiplicities. We also characterize the
recognizable series over a product monoid giving a
generalization of the Mezei's Theorem.}
}