1. For each of the following languages, prove that it is not regular. {an :n>0} (b)...

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1. For each of the following languages, prove that it is not regular. {an³ :n>0} (b) L₂= {abi ≥ 2j} L2 (a) L₁ = (c) L3= {w {a,b}* : na(w) #ni(w)} = 2. Given a language L over the alphabet Σ, define f(L) = {vo v € L, 0 € Σ, and v=uo for some u € [*} Prove that f(L) is regular if L is regular. 1. For each of the following languages, prove that it is not regular. {an³ :n>0} (b) L₂= {abi ≥ 2j} L2 (a) L₁ = (c) L3= {w {a,b}* : na(w) #ni(w)} = 2. Given a language L over the alphabet Σ, define f(L) = {vo v € L, 0 € Σ, and v=uo for some u € [*} Prove that f(L) is regular if L is regular.

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4 4n0 prove it is not regular by using pumping Step 1 Assume that language 4 as Step 2 consider stri... View the full answer