Regular Expressions
One day of describing regular language of via the notation of regular expressions. This notation involves
a combination of strings of symbols from some alphabet ∑, parentheses, and the operators +, ⋅, and *.
Formal definition: Let ∑ be a given alphabet. Then
- φ, λ and a ∈ ∑ are all regular expressions these are called primitive regular expressions.
- If r1 and r2 are regular expressions, so are r1 + r2, r1 ⋅ r2, r1* and (r1).
- A string is a regular expression if and only if it can be derived from the primitive regular expressions by a finite number of applications of the reuse in 92).
Operators of Regular Expressions:
- R* is kleene closure of regular expression R. (* is a unary operator)
- R+ is positive closure of regular expression R. (+ is a unary operator)
- ⋅ is concatenation operator. (⋅ is a binary operator)
- + is or operator. (+ is a binary operator)
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