多环幺半群的有理子集与价自动机
Rational subsets of polycyclic monoids and valence automata
摘要：
我们研究的语言类定义的价自动机与合理的目标集（或等价的，正规价文法与合理的目标集），其中的价幺半群是从重要的一类多环幺半群。我们表明，对于秩为2或更高的多环幺半群，这样的自动机完全接受上下文无关的语言。对于秩为1的多环幺半群（即双环幺半群），他们接受一类严格包括部分盲单计数器语言的语言。关键的证明是一个合理的子集的多环和双环monoids的描述，其他后果包括这些monoids的合理子集成员资格问题的可判定性，并关闭类的合理子集下的交叉和补充。
英文摘要：
We study the classes of languages defined by valence automata with rational target sets (or equivalently, regular valence grammars with rational target sets), where the valence monoid is drawn from the important class of polycyclic monoids. We show that for polycyclic monoids of rank 2 or more, such automata accept exactly the context-free languages. For the polycyclic monoid of rank 1 (that is, the bicyclic monoid), they accept a class of languages strictly including the partially blind one-counter languages. Key to the proof is a description of the rational subsets of polycyclic and bicyclic monoids, other consequences of which include the decidability of the rational subset membership problem for these monoids, and the closure of the class of rational subsets under intersection and complement.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
