Introduction to
Theory of Automata
By:
Wasim Ahmad Khan
Alphabet/Symbols/Character Set
A finite non-empty set of specific symbols
(letters), is called alphabet . It is denoted by
Greek letter ∑ (Sigma).
An alphabet is a finite set of symbols, usually
letters, digits, and punctuations.
Types of alphabet
1. Valid Alphabets
2. Invalid Alphabets
Valid Alphabet
If there is suffix but not prefix then it is a valid
Alphabet, While defining an alphabet of letters
consisting of more than one symbols, no letter
should be started with the letter of the same
alphabet.
Valid Alphabet :
  a, ba, c
Invalid Alphabet
If there is prefix present in an alphabet
then it is an invalid Alphabet.
Invalid Alphabet :   a, ab, c
String
Collection of characters/Combination of
symbols from an alphabet or sigma( ∑ )
OR
Finite Collection of Symbols
For Example
a+b & intabc both are strings.
Valid Strings
Language is a collection of Valid strings.
To declare strings symbols are basic things.
Criteria
All the character used to write a string must
belong to the character set of said language. It
must follow the “vary clear” rules defined by
said Language.
Restrictions of Character Set
1. It should not be included Capital lambda.
2. It should not be empty.
3. It must be finite.
Examples
∑ represents character set
∑={a,b}
I define a valid character set. Finite & non
empty.
∑ = { a , b , …}
Invalid
∑ = { 1 , 2 } Valid, Finite, Non Empty
Some Special Symbols
1. Sigma ∑
2. Capital Lambda Λ
3. Epsilon ε
Lexicographical Order
According to this strings are arranged in a set
length wise as indexing is used in dictionary .
∑={a,b}
Strings = aa , ab , ba , bb
∑={b,a}
Strings = bb , ba , ab , aa
Valid Lengths
 Smallest valid length is zero ( 0 )
 Largest valid length could be any length you can
made over sigma
Length of a string
Count of positions available to hold character.
∑ = { a , aa }
aaa its valid length could be 2 and 3.
Null String
String having length zero or a string having no position
at all.
Empty String
A String having no character at all
For example : { }
It creates a confusion so we mostly use phi φ .
Example 1
∑={a,b}
L = All the strings over the above sigma.
{ Λ , a , b , aa , ab , ba , bb , aaa , aab , aba , abb
, baa , bab , bba , bbb , …}
Note:
For continuation use only 3 dots.
Example 2
∑={a,b}
L = All the strings starting with ‘ a ’ over the
above sigma.
{ Λ , a , aa , ab , aaa , aab , aba , abb , …}