I have two grammars:
L → ε | aLcLc L → ε | aLcLc | LL
This two grammars are equals but the first one is regular, so it produces a regular language and a Finite State Automata. Instead, the second one is non regular but it might produces a regular language.
To prove it, I want to create two differentes automata: the first one should be a correct automata and if the second one can't be create then the language is not regular. Are all this statments correct?
If so, can someone help me build these two automata? Thank you!