Define the concept of a pushdown automaton with epsilon transitions.

Define the concept of a pushdown automaton with epsilon transitions.

A pushdown automaton with epsilon transitions, also known as an epsilon pushdown automaton (ε-PDA), is a type of automaton that extends the capabilities of a regular pushdown automaton (PDA) by allowing transitions to occur without consuming any input symbol. In addition to the stack and input tape, an ε-PDA has a set of epsilon transitions, which can be taken without reading any input symbol. These transitions can be used to perform spontaneous or non-deterministic actions, such as pushing or popping symbols on the stack, without requiring any input. The presence of epsilon transitions makes the ε-PDA more expressive and powerful than a regular PDA, allowing it to recognize a larger class of languages, including some non-context-free languages.