Introduction to automata theory. What is automata theory? why it is named so? History of Automata theory

1. Introduction
to Automata
Theory
-Sampath Kumar S,
AP/CSE, SECE

2. What is Automata Theory?
 Study of abstract computing devices, or
“machines”.
 Automaton = an abstract computing device
 Note: A “device” need not even be a physical
hardware!
 A fundamental question in computer science:
 Find out what different models of machines can do
and cannot do
 The theory of computation
 Computability vs. Complexity
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3. What is Automata ?
 The term "Automata" is derived from the
Greek word "αὐτόματα" which means "self-
acting".
 An automaton (Automata in plural) is an
abstract self-propelled computing device
which follows a predetermined sequence of
operations automatically.
Abstract: Existing in thought or as
an idea but not having a physical
or concrete existence.
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4. Alan Turing (1912-1954)
 Father of Modern Computer
Science
 British mathematician
 Studied abstract machines called
Turing machines even before
computers existed
 Heard of the Turing test?
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5. Theory of Computation: A
Historical Perspective
5
1930s • Alan Turing studies Turing machines
• Decidability
• Halting problem
1940-1950s
• “Finite automata” machines studied
• Noam Chomsky proposes the
“Chomsky Hierarchy” for formal
languages
1969
Cook introduces “intractable” problems
or “NP-Hard” problems
1970-
Modern computer science: compilers,
computational & complexity theory evolve
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6. Languages & Grammars
 Languages: “A language is a
collection of sentences of
finite length all constructed
from a finite alphabet of
symbols”
 Grammars: “A grammar can
be regarded as a device that
enumerates the sentences of
a language” - nothing more,
nothing less
 N. Chomsky, Information and
Control, Vol 2, 1959
6
Or “words”
Image source: Nowak et al. Nature, vol 417, 2002
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7. The Chomsky Hierarchy:
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Regular
(DFA)
Context-
free
(PDA)
Context-
sensitive
(LBA)
Recursively-
enumerable
(TM)
• A containment hierarchy of classes of formal languages
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8. Finite State Machine:
 An automaton with a finite number of states is
called a Finite Automaton(FA) or Finite State
Machine (FSM).
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9. Formal definition of a FSA:
An automaton can be represented by a 5-tuple (Q, ∑,
δ, q0, F), where −
 Q is a finite set of states.
 ∑ is a finite set of symbols, called the alphabet of
the automaton.
 δ is the transition function.
 q0 is the initial state from where any input is
processed (q0 ∈ Q).
 F is a set of final state/states of Q (F ⊆ Q).
Note: δ is called Delta and ∑ is called Sigma
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10. Finite Automaton classification:
Finite Automaton can be classified into two types −
 Deterministic Finite Automaton (DFA)
 Non-deterministic Finite Automaton (NDFA / NFA)
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11. Finite Automata : Examples
 On/Off switch
 Modeling recognition of the word “then”
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Start state Final stateTransition Intermediate
state
action
state
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12. Finite Automata
 Some Applications
 Software for designing and checking the
behavior of digital circuits
 Lexical analyzer of a typical compiler
 Software for scanning large bodies of text (e.g.,
web pages) for pattern finding
 Software for verifying systems of all types that
have a finite number of states (e.g., stock
market transaction, communication/network
protocol)
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14. நன்றி
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