Characterizing DFA languages

Question

How can we characterize DFA languages ?

Answer 1

It will be illustrated that the set of languages recognized by FA is closed under:

– union “C = (A ∪ B)”
– concatenation “C = (A ° B)”
– star “C = A* ”

Meaning: if A and B are the languages recognized by a DFA, then C is a language recognized by the DFA

• union “C = (A ∪ B)”
(A ∪ B) = {x : x ∈ A or x ∈ B or both}

• concatenation “C = (A ° B)”
(A ° B) = {xy: x ∈ A and y ∈ B}

• star “C = A* ” (note: ε always in A*)
A* = {x₁ x₂ x₃…x_k: k ≥ 0 and each x_i ∈ A}