History Of Automata Essay

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Automata?

It is plural of automaton simply define as "something that works automatically".

Example Of Automaton:
• Computer

Automata is concerned with mathematical models which are foundations of computing. These theoretical concepts will not vary with the next new model of computers.
A firm knowledge of the theoretical basis for computation will give you a stable platform from which to observes and understand the dazzling progress being made in the production of new computers and software..

History Of Automata:
In the 1930’s, Alan Turing (1912 – 1952), an English mathematician, studied an abstracts machine called Turing machine even before computers existed!
• He is regarded as pioneer of automata theory

Turing Machine:
The goal …show more content…

In the 1940’s and 1950’s, machines currently called “Finite Automata” were studied by a number of researchers:
• Initially proposed to model the brain function.
• Later used for variety of others purposes. 2. In late 1950’s, the Linguist N. Chomsky introduced formal grammar.
• Has close relationship to abstracts automata.
• Also important in development of software components and compiler. 3. In 1969, S. Cook extended the theory of Turing:
• what could be solved and what couldn’t.
Computability:
• S. Cook separated the solvable problems from those that can in principles be solved by a computer, but in practice, take so much time that computers are useless for all but very small instances of these problems.
• Latter class of problems are called “intractable or NP-hard.

• Complexity of Problems

Description Of Automata Theory:
Automata Theory is an interesting and in theoretical branch of computer science .Automata is the study of "abstract" computing devices machines and their algorithms.
• Also called theory of computation .irrelevant complications are dropped in order to focus on important concept.
• Automata theory help ensure the safety critical systems are correct.
• It helps create abstract models for …show more content…

•Length of string w is denoted as |w|
•Let w = 10011
–|w| = 5
–|ϵ| = ?
•0
–x = 01 ϵ 0 ϵ 1 ϵ 00 ϵ |x| = ?
•6
•xy = concatenation of two strings x and y
•ϵ being the identity for concatenation
•x is said to be prefix of y if xz = y for some z.
•z is said to be suffix of x if xz = y.

Language And Grammar:

•A language is a set of words.
•E.g.
–Given Σ = {0,1}, we may define a language L = {00, 01,10, - - -}.

•A grammar is a finite list of rules defining a language.
–Enumerates words of a language - nothing more, nothing less.

Powers Of An Alphabet:

•Σk = the set of all strings of length k
•E.g. Σ = {a, b, c}
–Σ1 = ? •{a, b, c}
–Σ2 = ?

•{aa, ab, ac, ba, bb, bc, ca, cb, cc}
–Σ0 = ? •{ϵ}

•The set of all strings over an alphabet Σ is denoted by Σ*
–Σ* = Σ0 U Σ1 U Σ2 U …

•E.g. Σ = {0, 1}, then Σ* = ?
–Σ* = {ϵ, 0, 1, 00, 01, 10, 11, 000, . . . } •The set of all non-empty strings over an alphabet Σ is denoted by Σ+
–Σ+ = Σ1 U Σ2 U … or equivalently,
–Σ* = {ϵ} U Σ+

Language:

•L is said to be a language over alphabet Σ only if L  Σ*
•Example
–Let L (defined over Σ = {0, 1}), be the language of all strings consisting of n 0’s followed by n

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