Question

Give context-free grammars that generate the following languages. In all parts the alphabet Σ is {0,1}.

a. w
b. w starts and ends with the same symbol
c. w

Answer 1

A context-free grammar (CFG) can be used to generate languages with specific properties. CFGs for languages containing at least three 1s, languages starting and ending with the same symbol, and languages with odd length are provided.

Step-by-step explanation:

A context-free grammar (CFG) is a set of production rules that define a language. Here are the CFGs that generate the given languages:

a. w
S -> 0S0 | 0S1 | 1S0 | 1S1 | 1
b. w starts and ends with the same symbol
S -> 0S0 | 1S1 | 0 | 1
c. the length of w is odd
S -> 0A0 | 1A1
A -> 0S0 | 1S1 | ε