2 research outputs found
Pumping Lemmata for Recognizable Weighted Languages over Artinian Semirings
Pumping lemmata are the main tool to prove that a certain language does not
belong to a class of languages like the recognizable languages or the
context-free languages. Essentially two pumping lemmata exist for the
recognizable weighted languages: the classical one for the Boolean semiring
(i.e., the unweighted case), which can be generalized to zero-sum free
semirings, and the one for fields. A joint generalization of these two pumping
lemmata is provided that applies to all Artinian semirings, over which all
finitely generated semimodules have a finite bound on the length of chains of
strictly increasing subsemimodules. Since Artinian rings are exactly those that
satisfy the Descending Chain Condition, the Artinian semirings include all
fields and naturally also all finite semirings (like the Boolean semiring). The
new pumping lemma thus covers most previously known pumping lemmata for
recognizable weighted languages.Comment: In Proceedings AFL 2023, arXiv:2309.0112