Pushdown Automata Concepts

Study Notes

Pushdown automata (PDA) extend nondeterministic finite automata by incorporating a stack for additional memory.
The stack enables PDAs to recognize non-regular languages, which finite automata cannot.
PDAs are equivalent in power to context-free grammars, allowing two methods to demonstrate a language's context-free nature: through context-free grammar or PDA recognition.

A schematic representation of a PDA includes control (states and transition function), an input tape, and a stack.
PDAs can "push" symbols onto the stack, shifting other symbols down, and "pop" symbols off the top, allowing for flexible information storage.
Unlike finite automata, PDAs can manage unbounded information, enabling the recognition of languages such as {0^n1^n | n ≥ 0}, which cannot be recognized by finite automata.

The PDA operates by reading input symbols sequentially.
For every '0' read, it pushes it onto the stack.
Upon encountering '1's, it pops one '0' for each '1' read.
The input is accepted if the stack is empty when the input ends; any deviations in stack status result in rejection.

A PDA’s formal definition includes input alphabet (Σ) and stack alphabet (Γ).
The transition function is determined by the current state, the next input symbol, and the top stack symbol.
Transitions can occur without reading from the input or stack, denoted by ε, which allows for flexibility in operation.
State diagrams illustrate PDA transitions similarly to finite automata, adjusted to incorporate stack operations (e.g., "a,b → c" indicates reading 'a', replacing top stack 'b' with 'c').

Push: Adding a symbol to the stack.
Pop: Removing the top symbol from the stack.
Stack: A storage mechanism that retains symbols in a last-in, first-out (LIFO) order, critical for recognizing context-free languages.