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 elimination of chain- and deletion rules depend on their inequational properties (and the idempotency of addition). It follows that these normal form theorems also hold in non-continuous semirings having enough fixed-points.
CITATION STYLE
Ésik, Z., & Leiß, H. (2002). Greibach normal form in algebraically complete semirings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2471, pp. 135–150). Springer Verlag. https://doi.org/10.1007/3-540-45793-3_10
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