PUSH DOWN AUTOMATA

A pushdown automaton (PDA) is a type of automaton that extends the capabilities of a finite automaton by adding a stack. It is used to recognize context-free languages, which cannot be recognized by finite automata alone.

DETERMINISTIC AND NON-DETERMINISTIC PDAs

There are two types of pushdown automata: deterministic (DPDA) and non-deterministic (NPDA).

- Deterministic PDA (DPDA): In a DPDA, for every input symbol and stack top symbol, there is at most one transition to a new state. This means that the next move is uniquely determined by the current state, the input symbol, and the stack top symbol.

- Non-deterministic PDA (NPDA): In an NPDA, there can be multiple transitions for the same input symbol and stack top symbol. The next move is not uniquely determined and the PDA can choose any of the possible transitions.

AT MOST ONE TRANSITION AROUND ALL CONFIGURATIONS

A pushdown automaton is said to have at most one transition around all configurations if, for any given combination of current state, input symbol, and stack top symbol, there is at most one transition that can be taken. This means that the PDA does not have multiple choices or ambiguity in its transitions.

In other words, a PDA is deterministic if, for any given configuration (current state, input symbol, and stack top symbol), there is a unique transition that can be taken. This allows the PDA to deterministically move from one configuration to the next without any ambiguity.

ANSWER: DETERMINISTIC (D)

The correct answer to the given question is option 'D', which is deterministic. A deterministic pushdown automaton has at most one transition around all configurations, ensuring that there is no ambiguity in its transitions.

Deterministic pushdown automata are particularly useful when dealing with context-free languages, as they allow for a clear and unambiguous recognition of these languages. The deterministic nature of the PDA ensures that it can deterministically move from one configuration to another, making it easier to analyze and understand its behavior.

Overall, a deterministic pushdown automaton is the correct answer because it satisfies the condition of having at most one transition around all configurations, providing a unique and deterministic behavior.