Automata Theory Questions
A two-way pushdown automaton (PDA) is a theoretical model of computation that extends the capabilities of a standard pushdown automaton. In a two-way PDA, the head of the reading device can move both left and right on the input tape, allowing it to read symbols in both directions.
Similar to a standard PDA, a two-way PDA consists of a finite set of states, an input alphabet, a stack alphabet, a transition function, and initial and final states. However, the key difference lies in the reading device's ability to move in both directions.
When processing an input string, the two-way PDA can perform the following operations:
1. Read a symbol from the input tape in the current position of the reading head.
2. Push a symbol onto the top of the stack.
3. Pop the top symbol from the stack.
4. Move the reading head one position to the left or right on the input tape.
The transition function of a two-way PDA determines the next state, the symbol to be pushed onto or popped from the stack, and the direction in which the reading head moves based on the current state and the symbol read from the input tape.
The acceptance of an input string by a two-way PDA depends on whether it can reach a final state after processing the entire input. The two-way PDA can accept the input by emptying the stack, indicating that the input string is accepted by the automaton.
Overall, the concept of a two-way pushdown automaton enhances the computational power of a standard pushdown automaton by allowing bidirectional movement on the input tape, enabling more complex language recognition and processing capabilities.