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Several Types of Representations for Series on Idempotent Semirings - or How to go beyond recognizability Keeping representability -

Ines Klimann
IFAC Proceedings Volumes 34 (13) 759 (2001)
DOI: 10.1016/S1474-6670(17)39085-7
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Some properties of recognizable Z-subsets

Nami Kobayashi
Theoretical Computer Science 293 (1) 83 (2003)
DOI: 10.1016/S0304-3975(02)00233-5
See this article