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Introduction to Automata Theory

1 Introduction to Automata TheoryReading: Chapter 12 What is Automata Theory ?nStudy of abstract computing devices, or machines nAutomaton = an abstract computing devicenNote:A device need not even be a physical hardware!nA fundamental question in computer science: nFind out what different models of machines can do and cannot donThe Theory of computationnComputability vs. Complexity3 Alan Turing (1912-1954)nFather of Modern Computer SciencenEnglish mathematiciannStudied abstract machines called Turing machineseven before computers existednHeard of the Turing test?(A pioneer of Automata Theory )4 Theory of Computation: A Historical Perspective1930s Alan Turing studies Turing machines Decidability Halting problem1940-1950s Finite Automata machines studied Noam Chomsky proposes the Chomsky Hierarchy for formal languages1969 Cook introduces intractable problemsor NP-Hard problems1970-Modern computer science: compilers, computational & complexity theoryevolve5 Languages & GrammarsOr words Image source: Nowak et al.

Recursively-enumerable (TM) •A containment hierarchy of classes of formal languages. 7 The Central Concepts of Automata Theory. 8 Alphabet An alphabet is a finite, non-empty set of symbols n We use the symbol ∑ (sigma) to denote an alphabet n Examples: n Binary: ∑ = {0,1}

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