Formal Languages Questions Medium
A deterministic pushdown automaton (DPDA) and a non-deterministic pushdown automaton (NPDA) are both types of finite state machines that have an additional stack component called a pushdown stack. However, they differ in terms of their behavior and capabilities.
The main difference between a DPDA and an NPDA lies in how they handle multiple possible transitions from a given state with a given input symbol and top of the stack symbol.
In a DPDA, for every state and input symbol, there is at most one possible transition to the next state, determined by the current state, input symbol, and top of the stack symbol. This means that the behavior of a DPDA is completely determined and predictable, as there is no ambiguity in the transition choices.
On the other hand, an NPDA allows for multiple possible transitions from a given state with a given input symbol and top of the stack symbol. This non-determinism means that an NPDA can have multiple paths to explore simultaneously during its computation. It can choose any of the possible transitions at each step, leading to different computation paths. This makes the behavior of an NPDA less predictable compared to a DPDA.
Another difference is that a DPDA accepts a language if there exists at least one computation path that leads to an accepting state, while an NPDA accepts a language if there exists at least one computation path that leads to an accepting state, regardless of the other possible paths.
In summary, the main differences between a DPDA and an NPDA are:
1. Determinism: A DPDA has a unique transition for each state, input symbol, and top of the stack symbol, while an NPDA can have multiple possible transitions.
2. Predictability: The behavior of a DPDA is completely determined and predictable, while an NPDA's behavior is less predictable due to non-determinism.
3. Acceptance: A DPDA accepts a language if there exists at least one computation path that leads to an accepting state, while an NPDA accepts a language if there exists at least one computation path that leads to an accepting state, regardless of the other possible paths.