Problem
Research questions and friction points this paper is trying to address.
Language Recognition
Fibrations
Factorisation System
Syntactic Quotients
J-limits
Languages and Recognition in a Category with Factorisation
🤖 AI Summary
本文通过在具有分解系统的范畴中使用纤维化方法，解决了语言识别问题，并研究了语言的句法商及闭包性质。
📝 Abstract
Language recognition by homomorphisms is a central construction of algebraic language theory. Initially studied for monoids and semigroups, it has subsequently been expanded to other algebraic structures. Our new categorical account is based on fibrations, which have already seen other applications in automata theory. Languages and surjective homomorphisms give indeed rise to two fibrations, and the notion of language recognition is stable under reindexing. We develop this framework in a category with a factorisation system and address two main technical questions in the fibrational setting. First, we provide sufficient conditions under which languages have syntactic quotients (which is a generalisation of syntactic congruences) and we show how such quotients can be described in some concrete cases using a result by Slomiński. Second, we introduce sufficient conditions under which (regular) languages are closed under certain J-limits and J-colimits.
Innovation
Methods, ideas, or system contributions that make the work stand out.
fibrations
syntactic quotients
J-limits and J-colimits
🔎 Similar Papers
No similar papers found.
