标题： 形式语言与带缺陷的拓扑量子场论 显示英文标题

标题： Formal Languages and TQFTs with Defects

摘要： 一种将带有缺陷的布尔1D TQFT分配给有限状态自动机的构造最近由Gustafson、Im、Kaldawy、Khovanov和Lihn开发。 我们证明该构造对于具有转换器作为态射的有限状态自动机范畴是函子性的。 某些子正则语言对应于相关TQFT上的额外上同调结构。 我们还表明，通过Melliès和Zeilberger提出的Chomsky-Schützenberger表示定理的范畴版本，该构造可以推广到上下文无关文法。 相应的TQFT则被描述为带有缺陷的余 bordism 操作数上的颜色操作数的态射。 显示英文摘要

摘要： A construction that assigns a Boolean 1D TQFT with defects to a finite state automaton was recently developed by Gustafson, Im, Kaldawy, Khovanov, and Lihn. We show that the construction is functorial with respect to the category of finite state automata with transducers as morphisms. Certain classes of subregular languages correspond to additional cohomological structures on the associated TQFTs. We also show that the construction generalizes to context-free grammars through a categorical version of the Chomsky-Sch\"utzenberger representation theorem, due to Melli\`es and Zeilberger. The corresponding TQFTs are then described as morphisms of colored operads on an operad of cobordisms with defects.