What are the closure properties of regular languages?
-
Union, Intersection and Complement Are The Closure Properties Of Regular Expressions
-
Suppose M1=(Q1,Σ,q1,A1,δ1) and M2=(Q2,Σ,q2,A2,δ2) accepts languages L1 and L2, respectively.
-
Let M be an FA defined by M=(Q,Σ,q0,A,δ), where
-
Q=Q1×Q1
-
q0=(q1,q2)
-
and the transition function δ is defined by the formula
-
δ((p,q),a)=(δ1 (p,a),δ2 (q,a))
-
for any pΣ Q1 and qΣ Q2 and a Σ then
-
if A={(p,q) | p∈A1 or q ∈ A2}, M accepts the language L1∪L2;
-
if A={(p,q) | p∈A1 and q ∈ A2}, M accepts the language L1∩L2;
-
if A={(p,q) | p∈A1 and q ∉A2}, M accepts the language L1 - L2;
