Closure Properties and Pushdown Automata in Automata Theory

Closure Properties

Regular languages preserved under specific operations.

Pushdown Automaton (PDA)

Computational model with stack for context-free languages.

Context-Free Grammar

Grammar allowing nested structures with non-terminals.

Regular Grammar

Simpler grammar subset of context-free grammars.

Regular Expression

Pattern defining a set of strings.

Derivation Process

Expanding start symbol to generate terminal strings.

Finite Automaton

State machine recognizing regular languages only.

Pumping Lemma

Proves a language is not regular.

Terminal

Basic symbols forming strings in CFG.

DFA Minimization

Reduces states while preserving language recognition.

Ambiguous Grammar

Grammar with multiple derivation trees for a string.

Acceptance State

Final state indicating string acceptance by PDA.

Unit Production

Production replacing one non-terminal with another.

Stack in PDA

Enables handling of nested structures and recursion.

Identity Production

Non-terminal replaced by itself in derivation.

Empty String Production

Non-terminal replaced with an empty string.

Context-Free Language

Language recognized by a PDA using a stack.

Recursive Structures

Languages requiring backtracking for proper parsing.

Finite Number of States

PDA has limited states but infinite stack space.

Language Recognition

Ability to determine if a string belongs to a language.

Production Rule

Defines how non-terminals can be replaced.

Transition Between States

Change of state based on input and stack.

Nested Dependencies

Complex language structures requiring context-free grammars.

Input Symbols

Characters read by automata during processing.

Accepting State

State where input string is accepted by automaton.

Chomsky Normal Form

Standard form for context-free grammars.

Mealy Machine

State machine with output based on state and input.

Moore Machine

State machine with output based solely on state.