# What is the difference between formal and informal languages?

## Language:

Set of strings with rules. It is a subset of Kleene Star ∑* for some alphabet ∑.

It can be finite or infinite

### Formal languages:

The language that is concerned with some rules or syntax and words of that language gives some meanings

### Informal languages:

The language that is concerned with only some rules or syntax not with meaning. The words of that kind of language have no meaning.

#### English Language

Learn          Lanre

•  Concerned with rules and meaning
•  Informal language or Semantic language

#### Language1: Starts with L and end with e

Learn          Lanre

•  Concerned with just rules or syntax, not with meaning
•  Formal language or syntactic language

An automaton focuses on formal languages

##### Alphabets:
• Finite set of letters or symbols are called alphabets
• ∑ = {a, b}, {0, 1}, {a, ab, baa}, {if, switch}
##### String
• Combination of finite alphabets forms a string
• S = ab, ba, bab, abb
##### Word
• String that belongs to some language is called word
• abbbb, bab, baaa  all belongs to language {a, b}
##### Null String
• String having no alphabet is called null string
• Represented by ε or λ
##### Length of string

Total number of alphabets in a string.

• S = {a, b}
• |S| = abb  length of the string is 3
• S = {a, ab}
• |S| = abab  length of the string is 2
• S = λ
• |S| = λ   length of the string is 0
##### Reverse of a string
• Represented by Rev(s) or sr
• S = {a,b}
• |S|= |abb|R = baa
• S = {a,ab}
• |S|= |aab|R = aba  ( “a” is s single letter and “ab” is another single letter, that’s why while reversing the string, “ab” will be written together as a whole and “a” will be written at the end for making it reversible)
##### Concatenation
• S1 = ab                 S2 = bb
• S1S2 = abbb
##### Union
• S1 = aa                 S2 = ba
• S1+S2 = aa + ba = ba + aa
• S1 = λ                   S2 = aa
• S1+S2 = λ  + aa = aa
##### Kleene star
• The kleene star is a unary operator on a set of strings or symbols that gives the infinite set of all possible strings of all possible lengths over S including λ or ε.
• It is represented by ∑*
• ∑ = {a, b}
• ∑* = { λ, a, b, ab, ba, aa, bb, ……………}
##### Kleene Closure / Plus
• The kleene plus or closure is a unary operator on a set of strings or symbols that gives the infinite set of all possible strings of all possible lengths over S excluding ε or λ.
• It is represented by ∑+
• ∑ = {a, b}
• += { a, b, ab, ba, aa, bb, ……………}

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