Theory of Computation TOC Automata and Its Power.

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Theory of Computation (TOC)

Automata and Its Power

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What is Automata?

An Automaton (plural: Automata) is an abstract machine that takes input strings and either accepts or rejects them based on a set of rules (transitions).

It is a mathematical model used to describe and analyze computation and languages.

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Why Study Automata?

• To understand what computers can and cannot do

• To classify languages by their complexity

• It forms the basis for compiler design, parsing, and language recognition

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Types of Automata & Their Power (Hierarchy)

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1. Finite Automata (FA):

• Types: DFA (Deterministic), NFA (Non-deterministic)

• Power: Can recognize regular languages

• Limitation: Cannot count or match nested patterns

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2. Pushdown Automata (PDA):

• Adds a stack to FA

• Recognizes context-free languages

• Example: Valid parentheses (()())

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3. Linear Bounded Automata (LBA):

• A restricted Turing machine with limited tape

• Recognizes context-sensitive languages

• More powerful than PDA

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4. Turing Machine (TM):

• Most powerful automaton

• Infinite memory (tape)

• Can simulate any computation

• Basis for real-world computers

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Chomsky Hierarchy (Power of Automata)

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What Automata Cannot Do:

• FA cannot recognize aⁿbⁿ

• PDA cannot recognize aⁿbⁿcⁿ

• TM cannot solve undecidable problems (like Halting Problem)

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Applications of Automata:

• Designing Compilers (Lexical analyzer uses FA)

• Syntax checking in programming languages (using PDA)

• Natural Language Processing

• Pattern matching and regular expressions

• AI algorithms in rule-based systems

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Theory of Computation TOC Automata and Its Power.

Introduction to Theory of Computation

Introduction to the Theory of Computation, 3rd ed.