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1. Let M be the PDA with states Q = {q0, q1, and q2}, final states F = {q1, q2} and transition function
δ(q0, a, λ) = {[q0, A]}
δ(q0, λ , λ) = {[q1, λ]}
δ(q0, b, A) = {[q2, λ ]}
δ(q1, λ , A) = {[q1, λ ]}
δ(q2, b, A) = {[q2, λ ]}
δ(q2, λ , A) = {[q2, λ ]}(a) Draw the state diagram for M.
(b) Using set notation, describe the language accepted by M.
(c) Trade a computation of the word aaaabb.
sin (cot -1 {cos (tan -1 x)}) tan -1 x = A => tan A =x sec A = √(1+x 2 ) ==> cos A = 1/√(1+x 2 ) so A = cos -1 (1/√(1+x 2 )) sin (cot -1 {cos (tan -1 x)}) = s
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