I am trying to construct a Deterministic Finite State Machine (DFSM) and a Context-Free Grammar (CFG) for the following language:
{ w \in {a, b}^* : w \notin { { a^n b^{2n} : n\geq 0 } } \
I am unsure how to properly design the FSM and CFG to capture these constraints.
How should I approach constructing a DFSM for this language?
What would be a step-by-step method to create a CFG that correctly represents it?
Are there any known techniques to handle constraints like a^n b^{2n} in FSMs and CFGs?
I would really appreciate a breakdown of the process or any helpful resources.
Thank you in advance for your help!
