2009/01/23 by Janusz Brzozowski, Brzozowski, J., Elyot Grant +3
Computer Science · Mathematics · #Advanced Algebra and Logic #Computational Complexity (cs.CC) #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Rings, Modules, and Algebras #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0901.3761
openalex publication_date 2009/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A famous theorem of Kuratowski states that in a topological space, at most 14 distinct sets can be produced by repeatedly applying the operations of closure and complement to a given set. We re-examine this theorem in the setting of formal languages, where closure is either Kleene closure or positive closure. We classify languages according to the structure of the algebra they generate under iterations of complement and closure. We show that there are precisely 9 such algebras in the case of positive closure, and 12 in the case of Kleene closure.