Question: Problem 2. PDAS In class, we defined E-DFA, E-NFA, E-RE, and E-CFG and proved they are all decidable. (a) Formulate a definition for E-PDA that

Problem 2. PDAS In class, we defined E-DFA, E-NFA, E-RE, and

Problem 2. PDAS In class, we defined E-DFA, E-NFA, E-RE, and E-CFG and proved they are all decidable. (a) Formulate a definition for E-PDA that is consistent with the definitions of these languages, and prove that E-PDA is decidable. Write out all details of the proof. (b) A PDA state is said to be unnecessary if the PDA never enters this state for any input string. Consider the problem of deciding if a given PDA has any unnecessary states. Formulate it as a language Hint: use the same strategy as we used for E-NFA UNNECESSARY-STATE-PDA, and then show that this language is decidable Hint: can you create a new PDA from the one given to you, so as to use it in a reduction, using your results from part (a)? Problem 2. PDAS In class, we defined E-DFA, E-NFA, E-RE, and E-CFG and proved they are all decidable. (a) Formulate a definition for E-PDA that is consistent with the definitions of these languages, and prove that E-PDA is decidable. Write out all details of the proof. (b) A PDA state is said to be unnecessary if the PDA never enters this state for any input string. Consider the problem of deciding if a given PDA has any unnecessary states. Formulate it as a language Hint: use the same strategy as we used for E-NFA UNNECESSARY-STATE-PDA, and then show that this language is decidable Hint: can you create a new PDA from the one given to you, so as to use it in a reduction, using your results from part (a)

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