Definition of Pushdown Automata (PDA) A Pushdown Automata (PDA) is a formal model that represents a finite-state machine (FSM) that can be used to determine...
Definition of Pushdown Automata (PDA)
A Pushdown Automata (PDA) is a formal model that represents a finite-state machine (FSM) that can be used to determine whether a given string of characters belongs to a language.
A PDA consists of the following components:
State machine: A finite set of states, each representing a specific condition or scenario.
Input stack: A stack-like structure that holds elements or tokens as the machine processes the string.
Transition function: A function that determines the next state and action to be taken based on the current state and the next input symbol.
Final state: A state that is reached when the input string is completely consumed and the machine reaches this state.
Example:
Consider a PDA with the following states:
Start state: Initial state, where the machine begins.
State 1: If the input is "a", the machine moves to state 2.
State 2: If the input is "b", the machine moves to state 3.
State 3: If the input is "c", the machine moves to state 1.
Final state: State 3, where the input string is completely consumed and the machine reaches this state.
Transitions:
From state 1, if the input is "a", the machine moves to state 2.
From state 2, if the input is "b", the machine moves to state 3.
From state 3, if the input is "c", the machine moves to state 1.
PDA can be used to determine if a given string belongs to a language:
Start at the initial state.
Read the first symbol of the input string.
Move to the corresponding state based on the transition function.
Repeat step 2 and continue processing the string.
If the input string is completely consumed and the machine reaches the final state, it accepts the input string. Otherwise, it rejects it