Automata

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AUTOMATA

1. What is an Automaton?

2. Fundamental Concepts

3. Finite-state Automaton

4. References

CONTENTS

1. The automaton (pl. automata) is an abstract computing machine, which is a conceptual model of the fundamentals of computation.

2. Automaton, originally from a Greek word αὐτόματον, means "self-acting".

3. The automaton arose in the 1950s out of Turing's (1936) model of algorithmic computation, considered by many to be the foundation of modern computer science.

WHAT IS AN AUTOMATON?

*Applications of automata

1. Text processing

2. Web browsing

3. Compiler

4. Operating system

5. Hardware design

6. Sequential logic circuits

7. etc.


<Recognition of a word 'then'>


q0 q1 q2 q3

t h e

q4

n

q0q1..q4 are states

't', 'h', 'e', 'n' are input alphabets

Blue-colored arcs are transitions between states

q0 is a start state

q4 is a final state


q0 q1 q2 q3

t h e

q4

n

If the automaton gets to the final state and there is no input left, it is said that the automaton accepts an input.

If the automaton never gets to the final state-it runs out of input or it gets some input that does not match an arc-it is said that the automaton rejects an input.


q0 q1 q2 q3

t h e

q4

n

<Recognition of regular expression /mee+~/>


q0 q1 q2 q3

m e e

q4

~e

<Recognition of English sentences>


and

q0 q1

q2

q4

theman is

q5

here

q3

men are

1. An alphabet is a set of symbols.

2. A string is a set of alphabets.

3. The set of all the strings accepted by an automaton is called the language recognized by the automaton.

4. A grammar is a formal counterpart of an automaton which is more focused on the aspect of the generation of a language.

5. The usefulness of an automaton for defining a language is that it can express an infinite set in a closed form.

FUNDAMENTAL CONCEPTS

1. An alphabet is a set of symbols.

2. A string is a set of alphabets.

3. The set of all the strings accepted by an automaton is called the language recognized by the automaton.

4. A grammar is a formal counterpart of an automaton which is more focused on the aspect of the generation of a language.

5. The usefulness of an automaton for defining a language is that it can express an infinite set in a closed form.

FUNDAMENTAL CONCEPTS

L(m) = {mee~, meee~, meeee~, meeeee~….}

The language characterized by a model m

(The regular expression /mee+~/, in this case.)

A finite-state automaton is defined by five parameters

A = (Q, ∑, q₀, F, δ)

Q = q₀ q₁q₂...qN-1: a finite set of N states.

∑ = a finite input alphabet of symbols.

q₀ = the start state, q₀ ∈ Q

F = the set of final states, F ⊆ Q

δ(q,i): the transition function between states. Given a state q ∈ Q and an input symbol i ∈ ∑, δ(q,i) returns a new state q′ ∈ Q. δ is thus a relation from Q × ∑ to Q.

FINITE-STATE AUTOMATON

김삼묘, 유기영. (2004). 계산모델: 오토마타 및 형식언어. 이한출판사

Jurafsky, D. and Martin, J. H. (2009). Speech and language processing 2nd Edition. Pearson Education, Inc.

Partee et al. (1993). Mathematical methods in linguistics. Kluwer Academic Publishers

REFERENCES

Automata

Science