Algebraic Laws for Regular Expressions RegEx

Algebraic Laws for Regular Expressions RegEx

Let us see the Algebraic Laws for Regular Expressions RegEx.

Associativity Laws for Regular Expressions RegEx

Let us see the Associativity Laws for Regular Expressions RegEx.

A + (B + C) = (A + B) + C and A.(B.C) = (A.B).C.

Commutativity for Regular Expressions RegEx

Let us see the Commutativity for Regular Expressions RegEx.

A + B = B + A. However, A.B 6= B.A in general.

Identity for Regular Expressions RegEx

Let us see the Identity for Regular Expressions RegEx.

∅ + A = A + ∅ = A and ε.A = A.ε = A

Annihilator for Regular Expressions RegEx

Let us see the Annihilator for Regular Expressions RegEx.

∅.A = A.∅ = ∅

Distributivity for Regular Expressions RegEx

Let us see the Distributivity for Regular Expressions RegEx.

Left distributivity:  A.(B + C) = A.B + A.C.

Right distributivity:  (B + C).A = B.A + C.A.
Idempotent A + A = A.

Closure Laws for Regular Expressions RegEx

Let us see the Closure Laws for Regular Expressions RegEx.

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(A*)* = A*, ∅* = ε, ε* = ε, A+ = AA* = A*A, and A* = A + + ε.

DeMorgan Type Law for Regular Expressions RegEx

Let us see the DeMorgan Type Law for Regular Expressions RegEx.

(L + B)* = (L*B*)*