Question

Consider the language \( L \) of all strings made of the symbols 0,1 and \( 2(\Sigma=\{0 \), \( 1,2\}) \) that contain the sequence 012 as a substring. a. [1 marks] Formally write down the alphabet of the language. b. [1 marks] Give one example of a string that is constructed from the correct alphabet, has a length of 6 , and that is in \( L \). Likewise, also give one example of such a string that is not in \( L \). c. [2 marks] Construct an FA whose language is \( L \). d. [2 marks] Give a Regular Expression (RE) for \( L \). e. [2 marks] From the RE, build a Context-Free Grammar (CFG) for \( L \). f. [2 marks] From the FA, build a regular grammar for \( L \).

          Consider the language \( L \) of all strings made of the symbols 0,1 and \( 2(\Sigma=\{0 \), \( 1,2\}) \) that contain the sequence 012 as a substring.
a. [1 marks] Formally write down the alphabet of the language.
b. [1 marks] Give one example of a string that is constructed from the correct alphabet, has a length of 6 , and that is in \( L \). Likewise, also give one example of such a string that is not in \( L \).
c. [2 marks] Construct an FA whose language is \( L \).
d. [2 marks] Give a Regular Expression (RE) for \( L \).
e. [2 marks] From the RE, build a Context-Free Grammar (CFG) for \( L \).
f. [2 marks] From the FA, build a regular grammar for \( L \).

Consider the language L of all strings made of the symbols 0,1 and 2(Σ={0, 1,2}) that contain the sequence 012 as a substring.
a. [1 marks] Formally write down the alphabet of the language.
b. [1 marks] Give one example of a string that is constructed from the correct alphabet, has a length of 6 , and that is in L. Likewise, also give one example of such a string that is not in L.
c. [2 marks] Construct an FA whose language is L.
d. [2 marks] Give a Regular Expression (RE) for L.
e. [2 marks] From the RE, build a Context-Free Grammar (CFG) for L.
f. [2 marks] From the FA, build a regular grammar for L.

Added by Linda W.

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