Introduction to PDA | Pushdown Automata Definition | Automata Theory & Formal Language | TOC | ATFL

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Pushdown Automata (PDA) is a type of automaton used in the theory of computation and formal language. It is an extension of finite automata that has a stack to store information during its computation.

A PDA can be formally defined as a 7-tuple (Q, Σ, Γ, δ, q0, Z, F), where:

Q is a finite set of states.
Σ is a finite set of input symbols, also known as the alphabet.
Γ is a finite set of stack symbols.
δ is a transition function that maps Q x (Σ ∪ {ε}) x Γ* to subsets of Q x Γ*, where ε represents the empty string and Γ* is the set of all possible strings that can be formed by the stack symbols.
q0 is the initial state.
Z is the initial stack symbol.
F is the set of final (or accepting) states.
A PDA reads an input string symbol by symbol from left to right, just like a finite automaton. However, it can also push and pop symbols onto its stack. The transition function δ takes into account the current state, the input symbol, and the top symbol on the stack to determine the next state and what to do with the stack. A PDA accepts an input string if there is a sequence of transitions that leads from the initial state to a final state while correctly manipulating the stack.

PDA has several applications in computer science, including parsing, the recognition of context-free languages, and the evaluation of programming language expressions.
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