(1) (a) Let r, 1, and r, be regular expression. Find all the regular ones from the following expression: 2, r'-0. ((r*). r), i-, +½. (b) Given a regular expression i = a(ab)* +b°a*, r, = (b + a) * +a*, find L(;) and L(r,), the languages associated with 7i and r2, respective ly. (c) Find a regular expression r such that L(r) is the same as L= {b"ab",(ba)*: n, m2 0,h2 1}.

5. Let L = {ablak | k>n+l}. a. List all strings of length 7. (use power notation: i.e. aabbbbaaaaaaaa is a²b¹a³)

Fast plz

For each of the following languages Ls {a, b}*, show that the elements of the infinite set {a"|n > 0} are pairwise L-distinguishable. (b) L={a'b' a*\k > i+ j}

For each of the following languages Ls {a, b}*, show that the elements of the infinite set {a"|n > 0} are pairwise L-distinguishable. (d) L= {a'b'\j is a multiple of i}

3. (a) Let Σ = {a, b}. Find a regular expression corresponding to the language L = {ba} ∗ ∪ {aa, bb}. (b) Let Σ = {0, 1}. Give the language corresponding to the regular expression 10∗ (0 +.

Use the Pumping Lemma to show that the the following language over {a,b,c}* is not CF  {wct | t ∈ {a,b}* ∧ w is a substring of t}

Make a conjecture whether or not it is regular and prove your assertion. When you prove a language is not regular, use the game with demon. Do not apply Pumping Lemma directly.

Not handwritten Given the language L denoted by r = (a+b)* . (aa*+b) and, ∑ = {a,b} and ∏ = {c,d,x} h(b) = xd, h(a) = cdx please provide the homomorphic image of the regular expression h(r)

(III) Assume the alphabet >= {a,b). Give the set all strings over Σ of length less than or equal to 2 including the null string. For each of the following languages, which of the above strings are in the language defined by the following regular expressions. (Show your work clearly). (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) a*b* a(ba)*b a* + b* (aaa)* (a+b)*a(a+b)*b(a+b)*a(a+b)* aba + bab (2 + a)b (a + ba + bb)(a+b)*