(b) What is the shortest word in * accepted by P? Show that your chosen word...

  

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(b) What is the shortest word in Σ* 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. -1 Q 9. Consider the context-free grammar G with terminal symbols T- {. y.c.¹, (,)}, non-terminal symbols N = {o. F. B), starting symbol o, and production rules F→BB-¹ B→ o + Fo | F →x|ye| (Fo) Note that we are regarding 1 as a single symbol. The string B1, for example, has length 2; it is the symbol B followed by the symbol -¹. (a) Give leftmost derivations in G for each of the following strings. (i) ee (ii) (ry)-¹(iii) gry-¹ (iv) x(er)-¹ (b) Use the method of Lecture SB to draw the transition diagram of a PDA accepting the language generated by G. State the input alphabet and the stack alphabet of your PDA. (c) Show how your PDA in (b) accepts the string (ay)-¹. Your answer to (a)(ii) will be useful. Q 10. Design a PDA accepting (021n | ne No}. You should specify your PDA with a transition diagram, and also clearly state your chosen stack alphabet. The following question is a proof question. It will be worth 2% of your final mark, so you are strongly advised to attempt it. (b) What is the shortest word in Σ* 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. -1 Q 9. Consider the context-free grammar G with terminal symbols T- {. y.c.¹, (,)}, non-terminal symbols N = {o. F. B), starting symbol o, and production rules F→BB-¹ B→ o + Fo | F →x|ye| (Fo) Note that we are regarding 1 as a single symbol. The string B1, for example, has length 2; it is the symbol B followed by the symbol -¹. (a) Give leftmost derivations in G for each of the following strings. (i) ee (ii) (ry)-¹(iii) gry-¹ (iv) x(er)-¹ (b) Use the method of Lecture SB to draw the transition diagram of a PDA accepting the language generated by G. State the input alphabet and the stack alphabet of your PDA. (c) Show how your PDA in (b) accepts the string (ay)-¹. Your answer to (a)(ii) will be useful. Q 10. Design a PDA accepting (021n | ne No}. You should specify your PDA with a transition diagram, and also clearly state your chosen stack alphabet. The following question is a proof question. It will be worth 2% of your final mark, so you are strongly advised to attempt it.

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Answer Part 1 Reviewing CFGs and PDAs CFGs ContextFree Grammars Define the structure and generation rules for strings in a language They consist of Te... View the full answer