Seminar Details

Regular languages constitute a simple class of languages that can be described via finite state automata. We explain a recently found enhancement of regular languages, extending them to an invariant of one-dimensional cobordisms (1-manifolds stretched between two0-manifolds) with decorations. This approach requires using a circular language as a regularizer and leads to a categorical extension of these familiar concepts. Various necessary concepts, including those of a cobordism, the Boolean semiring and semimodules over it, will be explained in the talk, which is based on a joint recent work with Mee Seong Im.