## 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) and many more.

## Descriptive definition of language

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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