Could you please help me with this question? Consider the language C = { w ∈...
Could you please help me with this question?
Consider the language C = { w ∈ {a, b} ∗| w contains at least as many as as bs }
For example, ǫ, aaa, aba, and bbaababaa are all in C, but bbb and bbaaabb are not.
a. Construct a 3-state push-down automaton to recognise C. Provide the solution as a transition diagram.
b. Prove formally that the following context-free grammar G generates C
S → ǫ | a | a S b | b S a | S S
Hint: Proceed in two steps; prove that every string in L(G) is in C (by structural induction) and prove that every string in C is in L(G) (by induction on the length of the string).
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Could you please help me with this question?
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