2015/03/07 by Brzozowski, Janusz, Davies, Sylvie
#FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL)
paper · doi:10.48550/arxiv.1503.02208
A (left) quotient of a language L by a word w is the language w-1L=\x| wx∈ L\. The quotient complexity of a regular language L is the number of quotients of L; it is equal to the state complexity of L, which is the number of states in a minimal deterministic finite automaton accepting L. An atom of L is an equivalence class of the relation in which two words are equivalent if for each quotient, they either are both in the quotient or both not in it; hence it is a non-empty intersection of complemented and uncomplemented quotients of L. A right (respectively, left and two-sided) ideal is a language L over an alphabet Σ that satisfies L=LΣ^* (respectively, L=Σ^*L and L=Σ^*LΣ^*). We compute the maximal number of atoms and the maximal quotient complexities of atoms of right, left and two-sided regular ideals.