## Descriptive definition of language – Explained with Examples

In the Theory of automata, languages can be defined with different techniques. Some of these are mentioned below;

- Language definition by using the Descriptive definition
- Language definition by using the Recursive definition
- Language definition by using the Regular Expressions (RE)
- Language definition by using the Finite Automaton(FA)

## Descriptive definition of language

In Descriptive definition of language, we describe the conditions imposed on its words.

The language can be defined and we can generate the strings but only the string of the given language.

## Examples of Descriptive definition of language

### Example 1 of Descriptive definition of language

**Descriptive definition of the language **of strings of odd length, defined over Σ={a}, can be defined as

L={a, aaa, aaaaa,…..}

### Example 2 of Descriptive definition of language

**Descriptive definition of the language **of strings of even length, defined over Σ={a}, can be defined as

L={aa, aaaa, aaaaaa, aaaaaaaa…..}

### Example 3 of Descriptive definition of language

**Descriptive definition of the language** of strings that must start with a, defined over Σ ={a,b,c}, can be defined as L ={a, ab, aa, aba, abb, ac, acc, ….}

### Example 4 of Descriptive definition of language

**Descriptive definition of the language** of strings that does not start with a, defined over Σ ={a,b,c}, can be defined as L ={Λ, b, c, ba, bb, bc, ca, cb, cc, …}

### Example 5 of Descriptive definition of language

**Descriptive definition of the language** **of t**he strings of length 1, defined over Σ ={X,Y,Z}, can be defined as

L={X, Y, Z }

### Example 6 of Descriptive definition of language

**Descriptive definition of the language** **of t**he strings of length 2, defined over Σ ={X,Y,Z}, can be defined as

L={XX, XY, XZ,YX, YY,YZ,ZX,ZY,ZZ, …..}

### Example 7 of Descriptive definition of language

**Descriptive definition of the language** of the strings of length 3, defined over Σ ={X,Y,Z}, can be defined as

L={XXX, XYY, XZY,YXX, YYY,YZZ, …. }

### Example 8 of Descriptive definition of language

**Descriptive definition of the language** L of strings ending in a, defined over Σ ={a,b}, can be defined as

L={a,aa,ba,aaa,aba,baa,bba,…}

### Example 9 of Descriptive definition of language

**Descriptive definition of the language** **EQUAL**, of strings with a number of 0’s equal to the number of 1’s, defined over Σ={0,1}, can be defined as

{Λ ,01,0011,0101,1010,0110,…}

### Example 10 of Descriptive definition of language

**Descriptive definition of the language** of **EVEN-EVEN** , of strings with even number of a’s and even number of b’s, defined over Σ={a,b}, can be defined as

{Λ, aa, bb, aaaa,aabb,aabb, abba, baba, bbaa, ,…}

### Example 11 of Descriptive definition of language

**Descriptive definition of the language** of a^{n}b^{n} and of strings defined over Σ={a,b}, as

{a^{n} b^{n} : n=1,2,3,…}, can be defined as

{ab, aabb, aaabbb,aaaabbbb,…}

When n=1, then ab

When n=2, then aabb

When n=3, then aaabbb

When n=4, then aaaabbbb

### Example 12 of Descriptive definition of language

**Descriptive definition of the language** of a^{n}b^{2}^{n} and of strings defined over Σ={a,b}, as

{a^{n} b^{2}^{n} : n=1,2,3,…}, can be defined as

{ abb, aabbbb, aaabbbbbb, aaaabbbbbbbb,…}

When n=1, then abb

When n=2, then aabbbb

When n=3, then aaabbbbbb

When n=4, then aaaabbbbbbbb

### Example 13 of Descriptive definition of language

**Descriptive definition of the language** of a^{n}b^{3}^{n} and of strings defined over Σ={a,b}, as

{a^{n} b^{3}^{n} : n=1,2,3,…}, can be defined as

{ abbb, aabbbbbb, aaabbbbbbbbb , aaaabbbbbbbbbbbb,…}

When n=1, then abbb

When n=2, then aabbbbbb

When n=3, then aaabbbbbbbbb

When n=4, then aaaabbbbbbbbbbbb

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