Question

Q8. Consider the context-free grammar G with terminal symbols T = {x, y, e, ^{-1}, (, )}, non-terminal symbols N = {sigma, F, B}, starting symbol sigma, and production rules sigma o Fsigma mid F F o B mid B^{-1} B o x mid y mid e mid (Fsigma) Note that we are regarding $^{-1}$ as a single symbol. The string $B^{-1}$, 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) $e^{-1}$ (ii) $y^{-1}x^{-1}$ (iii) $xyx^{-1}y^{-1}$ (b) Use the method of Lecture 8B 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 $y^{-1}x^{-1}$. Your answer to (a)(ii) will be useful.

          Q8. Consider the context-free grammar G with terminal symbols T = {x, y, e, ^{-1}, (, )}, non-terminal symbols N = {sigma, F, B}, starting symbol sigma, and production rules
sigma 	o Fsigma mid F
F 	o B mid B^{-1}
B 	o x mid y mid e mid (Fsigma)
Note that we are regarding $^{-1}$ as a single symbol. The string $B^{-1}$, 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) $e^{-1}$ (ii) $y^{-1}x^{-1}$ (iii) $xyx^{-1}y^{-1}$
(b) Use the method of Lecture 8B 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 $y^{-1}x^{-1}$. Your answer to (a)(ii) will be useful.

Q8. Consider the context-free grammar G with terminal symbols T = x, y, e, ^-1, (, ), non-terminal symbols N = sigma, F, B, starting symbol sigma, and production rules
sigma o Fsigma mid F
F o B mid B^-1
B o x mid y mid e mid (Fsigma)
Note that we are regarding ^-1 as a single symbol. The string B^-1, 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) e^-1 (ii) y^-1x^-1 (iii) xyx^-1y^-1
(b) Use the method of Lecture 8B 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 y^-1x^-1. Your answer to (a)(ii) will be useful.

Added by Raymond S.

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