一句话：引入多项式自动机，刻画其零性问题的复杂度，并应用于 VAS 覆盖性与流式字符串转换器等价性。
本文引入多项式自动机，作为域上加权自动机的推广。核心问题是零性问题：判定给定自动机是否在所有词上输出零。作者分析其复杂度，证明一般情形下该问题非原始递归；进而刻画出一个子类，使零性问题为原始递归。进一步限定后，得到仿射 VAS 的一个子类，其覆盖性可在 2EXPSPACE 内判定。作为应用，利用多项式自动机给出流式字符串转换器等价性可判定的新证明，并证明无拷贝流式字符串转换器的等价性属于 PSPACE。
We introduce a generalisation of weighted automata over a field, called polynomial automata, and we analyse the complexity of the Zeroness Problem in this model, that is, whether a given automaton outputs zero on all words. While this problem is non-primitive recursive in general, we highlight a subclass of polynomial automata for which the Zeroness Problem is primitive recursive. Refining further, we identify a subclass of affine VAS for which coverability is in 2EXPSPACE. We also use polynomial automata to obtain new proofs that equivalence of streaming string transducers is decidable, and that equivalence of copyless streaming string transducers is in PSPACE.