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 :

Invalid Alphabet If there is prefix present in an alphabet then it is an invalid Alphabet. Invalid Alphabet :

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, …}