I figured out that the CFG that starts and ends with the same symbol in alphabet $\Sigma=\{0,1\}$ will be : S -> 0A0|1A1|0|1|

A -> 0A|1A|𝜖

How can i interpret the odd number of 1's also?

  • $\begingroup$ Let $B$ be the set of all strings with an even number of 1's, and $C$ the set of all strings with an odd number of 1's. Write productions for $B$ and $C$ (depending on each other). Then figure out how to modify the $S$ you already wrote. $\endgroup$
    – Joppy
    Nov 23 '20 at 22:39
  • $\begingroup$ Your language is regular. Construct a regular expression and convert it to a context-free grammar. $\endgroup$ Nov 23 '20 at 22:51

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