Descriptive definition of language – Explained with Examples
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 the 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 the 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 anbn and of strings defined over Σ={a,b}, as
{an bn : 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 anb2n and of strings defined over Σ={a,b}, as
{an b2n : 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 anb3n and of strings defined over Σ={a,b}, as
{an b3n : 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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