Automata Theory Questions
A deterministic pushdown automaton (DPDA) is a theoretical model of computation that extends the concept of a deterministic finite automaton (DFA) by incorporating a stack. It consists of a finite set of states, an input alphabet, a stack alphabet, a transition function, an initial state, and one or more final states.
At each step, the DPDA reads an input symbol, checks the top symbol of the stack, and based on the current state, input symbol, and stack symbol, it determines the next state, the symbol to be pushed onto the stack (if any), and the symbol to be popped from the stack (if any). The transition function maps the current state, input symbol, and stack symbol to the next state, stack symbol(s), and the direction of stack movement.
Unlike a non-deterministic pushdown automaton (NPDA), a DPDA has a unique transition for each combination of current state, input symbol, and stack symbol. This means that given the current state and input symbol, the DPDA can always determine the next state and stack operation deterministically.
The acceptance of a string by a DPDA is determined by reaching a final state after processing the entire input. The DPDA accepts the input if there exists at least one sequence of transitions that leads to a final state. If no such sequence exists, the input is rejected.
In summary, a deterministic pushdown automaton is a computational model that uses a stack to extend the capabilities of a deterministic finite automaton, allowing it to recognize context-free languages.