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1. (3 pts) What is the basic idea for how to convert an arbitrary context-free grammar into an equivalent push-down automaton? Explain what the state(s) correspond to, and what the transition(s) correspond to.
   
   
   
   
   
   
   
   
   
   
2. (1 pt) True or False: Every push-down automaton can be converted into an equivalent deterministic push-down automaton.
   
   
   
   
3. (1 pt) True or False: There exists an inherently ambiguous language that is accepted by some deterministic push-down automaton.