Annals of Pure and Applied Logic 133 (1-3):173-203 (2005)

We give inequational and equational axioms for semirings with a fixed-point operator and formally develop a fragment of the theory of context-free languages. In particular, we show that Greibach’s normal form theorem depends only on a few equational properties of least pre-fixed points in semirings, and eliminations of chain and deletion rules depend on their inequational properties . It follows that these normal form theorems also hold in non-continuous semirings having enough fixed points
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DOI 10.1016/j.apal.2004.10.008
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