Conversion of NDPDA to DPDA

Definition:
- NDPDA (Nondeterministic Pushdown Automaton) is a type of automaton that can have multiple possible transitions for a given input symbol and stack top symbol combination.
- DPDA (Deterministic Pushdown Automaton) is a type of automaton where for every input symbol and stack top symbol combination, there is at most one possible transition.

Conversion Process:

NDPDA to DPDA:
1. In an NDPDA, for a given input symbol and stack top symbol combination, there can be multiple possible transitions.
2. To convert an NDPDA to a DPDA, we need to ensure that for each input symbol and stack top symbol combination, there is at most one possible transition.
3. This is achieved by determinizing the NDPDA, which involves eliminating the nondeterminism by creating equivalent deterministic states.
4. Determinization involves creating a new state for each unique combination of current state, input symbol, and stack top symbol.
5. The transitions from these new states are determined based on the possible transitions in the NDPDA.
6. The resulting automaton is a DPDA, where for each input symbol and stack top symbol combination, there is at most one possible transition.

Why Conversion is not Possible (algorithmically) from NDPDA to DPDA:
- The conversion from NDPDA to DPDA is not always possible algorithmically.
- This is because the number of states in the resulting DPDA can be exponentially larger than the number of states in the original NDPDA.
- This exponential blow-up in the number of states can make the conversion algorithmically infeasible for certain cases.
- Therefore, there is no general algorithm that can convert any NDPDA to a DPDA.

Conclusion:
- The conversion from NDPDA to DPDA is not possible algorithmically due to the potential exponential blow-up in the number of states.
- This makes it a non-trivial task to convert an NDPDA to a DPDA, and it may not be feasible for certain cases.