Question

**Use the pumping lemma to show that {w | w belongs to {a,
b}*,and w is a palindrome of even length.} is not
regular.**

Answer #1

Use the pumping lemma to show that the following languages are
not regular.
b. A2 = {www| w € {a, b}*}

Prove that the following languages are not regular using pumping
lemma:
(a) {w : w != wR}
(b) {ai bjak : k ≤ i + j}

Use pumping lemma to prove that L3a = {ab^m ab^m a| m>0} is
non-regular

if f belongs to R[a,b] and k belongs to R show that kf belongs
to R[a,b]

Consider the language L3 over alphabet Σ = { a, b }, L3 = { w ∈
Σ* | w is a palindrome of any length}.
Construct a PDA that recognizes L3.
Implement that PDA in JFLAP

Use induction to prove that if b belongs to a ring and m is a
positive integer, then m(−b) = −(mb).
Notice that -(mb) is the additive inverse of mb, so mb+m(-b)=0.
Also keep in mind that m is not a ring element

Let a,b,c be integers with a + b = c. Show that if w is an
integer that divides any two of a, b, and c, then w will divide the
third.

a. Let T : V → W be left invertible. Show that T is
injective.
b. Let T : V → W be right invertible. Show that T is
surjective

Prove that the language A\B = {w: wx ∈ A, X ∈ B}, where A is a
CFL and B is regular is a CFL.

Show that if G is a CFG in Chomsky normal form, then for any
string w is a member of L(G) of length n >=1, exactly 2n-1 steps
are required for any derivation of w.

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