Regular expression
A regular expression can be defined as the following properties.
Kleene Star Closure:
Kleene star closure can be shown as
∑ = Set of Alphabet
∑* = Set of all combination of sigma alphabet
For the example ∑ and ∑* can be described as following:
∑ ∑*
{a} {a}* = φ, a, aa, aaa, aaaa, aaaaa……..
{ab} {ab}*= ab, abab, ababab……..
{aa} {aa}*= aa, aaaa, aaaaaa……..
Plus Operator:
It is same to the sigma staric but it does not contains the “φ” operator.
{a}₊ = a, aa, aaa, aaaa, aaaaa……
OR Operator:
OR operator have the following properties:
(a+b)
(a+b)* = φ, a, b, aa, ab, bb, aba….
(a+b)+ = a, b, aa, ab, bb, aba….
(a+b)*a+ = ending must be on a that is a, aa, ba, bba, aaa….
- In Regular expression, we usually use the “*”, “+” operators.
- One language can contain more than one regular expression.
- But the one Regular expression can be represent only one language.
- a(a+)* language staring from ä
- a(a+)*ä language starting and ending at ä
- ((a+b)(a+b)) even string generating language
- ((a+b)(a+b))*(a+b) odd string generating language.
The rule for descriptive to RE:
The rules for descriptive to RE are as follows:
- All the strings formed by descriptive way of the language L1 must be contained in the RE way of language L1.
- Language L upon ∑={a,b} containing double aa
Our result should be aa, aaa, aab, baa, aaaa, aaaab, abaa…..
RE of this language will be in this form (a+b)*aa (a+b)*:
- Both languages should generate an exact sequence of the alphabet in equivalency.
