Q7. What is the order of Sg? Find the smallest n N such that o -...

  

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Q7. What is the order of Sg? Find the smallest n N such that o" - id for every o Sg. Justify your answer. Hint: Think of each a expressed as disjoint cycles. Q8. Let P be the following PDA with input alphabet - (0.1) and stack alphabet T-{0, 1.}. 0.816 1.18 90 6,8 + 11 8 91 1,00 0, 0 (92) (a) Show how P processes the following words, indicating whether they are accepted or rejected. Assume that P always transitions from qo to q₁ in the first step of the computation (for this particular PDA, this ensures that there is a unique way to process a given input). (i) 1011 (ii) 00110 (iii) 101101 (iv) 110100 (b) What is the shortest word in E accepted by P? Show that your chosen word is accepted. (c) Is the language L(P) accepted by P a regular language? If so, give a regular expression. If not, explain why not. Q7. What is the order of Sg? Find the smallest n N such that o" - id for every o Sg. Justify your answer. Hint: Think of each a expressed as disjoint cycles. Q8. Let P be the following PDA with input alphabet - (0.1) and stack alphabet T-{0, 1.}. 0.816 1.18 90 6,8 + 11 8 91 1,00 0, 0 (92) (a) Show how P processes the following words, indicating whether they are accepted or rejected. Assume that P always transitions from qo to q₁ in the first step of the computation (for this particular PDA, this ensures that there is a unique way to process a given input). (i) 1011 (ii) 00110 (iii) 101101 (iv) 110100 (b) What is the shortest word in E accepted by P? Show that your chosen word is accepted. (c) Is the language L(P) accepted by P a regular language? If so, give a regular expression. If not, explain why not.