循环半花自动机的句法复杂性
Syntactic Complexity of Circular Semi-Flower Automata
摘要：
我们研究了自由幺半群的某些类型的生成子幺半群的句法复杂性。实际上，我们考虑的是那些被循环半花自动机（CSFA）接受的子幺半群。在这里，我们表明，在最多一个“分支点”（BPI）的CSFA的语法复杂性是线性的。进一步证明了在二进制字母表上具有两个bpi的$n$状态CSFA的语法复杂度为$2n(n+1)$ .
英文摘要：
We investigate the syntactic complexity of certain types of finitely generated submonoids of a free monoid. In fact, we consider those submonoids which are accepted by circular semi-flower automata (CSFA). Here, we show that the syntactic complexity of CSFA with at most one `branch point going in' (bpi) is linear. Further, we prove that the syntactic complexity of $n$-state CSFA with two bpis over a binary alphabet is $2n(n+1)$.
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