Quotient complexities of atoms in regular ideal languages

  • Janusz Brzozowski
  • Sylvie Davies


A (left) quotient of a language L by a word w is the language w −1L = {x | wx ϵ 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.


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How to Cite
Brzozowski, J., & Davies, S. (2015). Quotient complexities of atoms in regular ideal languages. Acta Cybernetica, 22(2), 293-311. https://doi.org/10.14232/actacyb.22.2.2015.4
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