We present pumping lemmas for five classes of functions definable by fragments of weighted automata over the min-plus semiring, the max-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of functions definable by unambiguous, finitely-ambiguous, polynomially-ambiguous weighted automata, and the full class of weighted automata is strict for the min-plus and max-plus semirings.
翻译:我们提出五类功能的抽泵列母体,这些功能可以通过微增半衰期、最大加半衰期和自然数字的半衰期的加权自动数据碎片来定义。 作为必然结果,我们表明,对微增半衰期和最大加半衰期来说,可明确、有限、明确、多元性、多元性、多元性、多元性、多元性、全等加权自动数据组和全等加权自动数据组来说,对微增和最大半衰期来说是严格的。