Using pumping lemma prove that the language A = {yy | y E {0,1}* } is not regular.

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}

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}

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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.

Design a Pushdown Automaton to accept the language anbn for n≥2. Submit the following: Analysis of the problem Algorithmic principles Solution PDA

5. Find a closed form representation for the function defined recursively by f(0) = 5 and f(n+1)=2f(n)+4". Prove that your representation is correct using an inductive argument.

If the languages are regular, give an automaton. Otherwise, show it is notregular by using pumping lemma. L = {b2anbma3 | m = n}.

Let Σ={a,b}. For each of the following languages over Σ, prove that the language is regular (a)  La​={w∈Σ∗:n0​(w)is divisible by 4 andwends in aab}

Let L be the language L={aPb9cds | pq and q#r} over the alphabet Σ={a,b,c,d). Prove that L is not regular using the pumping lemma. Note: Follow the mathematical formalism given in the textbook. Explain your steps.