Question

1. Give context-free grammars generating each of the following languages over Σ = {0, 1}:

1. {w : |w| ≤ 5}
2. {w : |w| > 5 or its third symbol is 1}
3. {w : every odd position of w is 1}

Answer 1

context free grammar {= {0, 1} {w: (w/<5} SAAAAA A - 0/11€ Examples of strings generated by above language {0,000, 01010,11111. }

{w: /w/>5 or its third symbol is I} SAAB В — с/р CIE E OE/IE/E D → AAAAE A - 0/1 Examples 2001, 101, 00011, ----}

{w: Every odd position of wis 1} - IA A → 05/15/011 Examples {10,101, IIII....}