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Automata theory - Wikipedia

This Wikipedia page provides a foundational overview of Automata Theory, a core subject in computer science. It explains what automata are, their formal definitions, and various types studied, serving as an introductory resource for understanding computational models.

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收录于

2026年3月17日

学科与领域

computer-science-fundamentals · theory-of-computation

年级范围

九年级（高一）–十二年级（高四）

页面类型

Article

简介

Automata Theory: Overview and Foundations

  • Definition: Automata theory is the study of abstract, self-propelled computing devices (automata) that follow predetermined sequences of operations. It is a core discipline in theoretical computer science with roots in mathematical logic and cognitive science.
  • Core Components: An automaton is formally defined by its input alphabet, output alphabet, set of states, transition function (next-state), and output function.
  • Key Concepts:
    • Finite Automata (FA/FSM): Machines with a finite number of states that transition based on input symbols.
    • Formal Languages: Automata act as finite representations of formal languages; the set of words accepted by an automaton is the "language recognized" by that machine.
    • Chomsky Hierarchy: A classification system describing the nesting relationship between major classes of automata and formal grammars.
    • Run: The sequence of states an automaton traverses while processing an input word.
  • Historical Development:
    • Emergence as an autonomous discipline occurred in the mid-20th century.
    • 1956: A pivotal year featuring the publication of Automata Studies (contributions by Shannon, von Neumann, Minsky, Kleene, etc.) and Noam Chomsky’s work on the Chomsky hierarchy.
    • 1960s: Development of "structure theory" (algebraic decomposition) and computational complexity theory.
  • Applications: Automata are essential in compiler construction, artificial intelligence, parsing, formal verification, and the theory of computation.
  • Variations of Automata:
    • Input types: Finite sequences, infinite words ($\omega$-automata), and tree structures (tree automata).
    • State types: Single-state (combinational circuits), finite-state, and infinite-state machines (e.g., Turing machines, pushdown automata).
  • Notable Theorems:
    • Myhill–Nerode Theorem: Provides conditions for a language to be regular and counts states in a minimal machine.
    • Pumping Lemma: A tool used to prove properties of regular languages.
    • Equivalence: The computational equivalence of deterministic and nondeterministic finite automata.
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