10. Context-Free Languages & Lexers

For each context-free grammar G:

1. describe L(G)
   
2. algoritmically construct a PDA that accepts the same language
   
3. is the grammar ambiguous? If yes, write a non ambiguous grammar that generates the same language
   
   1. $ S \leftarrow aS | aSb | \epsilon $
      
      
   2. $ S \leftarrow aAA \\ A → aS | bS | a $
      
   3. $ S \leftarrow ABC \\ A \leftarrow aA | \epsilon \\ B \leftarrow bbB | b \\ C \leftarrow cC | c$

Given the following specs, construct the lexer DFA as presented in lecture 14 [1]:

• PAIRS: $ (10 | 01)* $
• ZERO_ONES: $ 01+ $
• NO_CONSEC_ONE: $ (1 | \epsilon)(01 | 0)* $

Separate the following input strings into lexemes:

[1] https://curs.upb.ro/2022/pluginfile.php/420515/mod_resource/content/0/L14-lexers.pdf