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Regular Expression
For instance: In a regular expression, x* means zero or more occurrence of x. It can generate {e, x, xx, xxx, xxxx, .....} In a regular expression, x^{+} means one or more occurrence of x. It can generate {x, xx, xxx, xxxx, .....} Operations on Regular LanguageThe various operations on regular language are: Union: If L and M are two regular languages then their union L U M is also a union. 1. L U M = {s  s is in L or s is in M} Intersection: If L and M are two regular languages then their intersection is also an intersection. 1. L ⋂ M = {st  s is in L and t is in M} Kleen closure: If L is a regular language then its Kleen closure L1* will also be a regular language. 1. L* = Zero or more occurrence of language L. Example 1:Write the regular expression for the language accepting all combinations of a's, over the set ∑ = {a} Solution: All combinations of a's means a may be zero, single, double and so on. If a is appearing zero times, that means a null string. That is we expect the set of {ε, a, aa, aaa, ....}. So we give a regular expression for this as: R = a* That is Kleen closure of a. Example 2:Write the regular expression for the language accepting all combinations of a's except the null string, over the set ∑ = {a} Solution: The regular expression has to be built for the language L = {a, aa, aaa, ....} This set indicates that there is no null string. So we can denote regular expression as: R = a^{+} Example 3:Write the regular expression for the language accepting all the string containing any number of a's and b's. Solution: The regular expression will be: r.e. = (a + b)* This will give the set as L = {ε, a, aa, b, bb, ab, ba, aba, bab, .....}, any combination of a and b. The (a + b)* shows any combination with a and b even a null string.
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