# 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|
^{R }= |abb|^{R}= baa

- |S|
- S = {a,ab}
- |S|
^{R }= |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)**

- |S|

**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, ……………}

- ∑