2013/08/31 by Janusz Brzozowski, Gareth Davies
Computer Science · #cs.FL
paper · pdf · doi:10.4204/eptcs.151.10
published as EPTCS 151, 2014, pp. 151-161 · In Proceedings AFL 2014, arXiv:1405.5272
arxiv created 2014/05/22 · arxiv updated 2014/05/23
The atoms of a regular language are non-empty intersections of complemented and uncomplemented quotients of the language. Tight upper bounds on the number of atoms of a language and on the quotient complexities of atoms are known. We introduce a new class of regular languages, called the maximally atomic languages, consisting of all languages meeting these bounds. We prove the following result: If L is a regular language of quotient complexity n and G is the subgroup of permutations in the transition semigroup T of the minimal DFA of L, then L is maximally atomic if and only if G is transitive on k-subsets of 1,...,n for 0 <= k <= n and T contains a transformation of rank n-1.