Question: 1. Fix the alphabet ? = {0 , 1} for all strings. Let x,y be fixed strings. Let L x = y be the language

1. Fix the alphabet ? = {0,1} for all strings. Let x,y be fixed strings. Let Lx=y be the language of all strings w such that the number of occurrences of x in w is the same as that of y in w. Show that for any two strings x,y, Lx=y is a DCFL.

2. Same as Question above, but define Lx=y=z where the number of occurrences of x,y,z in w is the same. Is Lx=y=z always context-free? Explain.

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