Kleene Closure | Positive Closure | Language | Basic Concepts of Automata
Kleene Closure/Kleene Star:
- Kleene Closure is the infinite set of all possible strings of all possible lengths including Ɛ
- It is denoted by ∑*
- So ∑*=∑0 U ∑1 U ∑2 U ∑3U…..
- For example over ∑= {0,1}
Positive Closure:
- Positive closure is the infinite set of all possible strings of all possible lengths excluding Ɛ
- It is denoted by ∑+
- So ∑+=∑* - { Ɛ }
- So ∑+= ∑1 U ∑2 U ∑3U…..
- For example over ∑= {0,1}
∑* ={ 0,1,00,01,10,11, 000,001,010,011,100,101,110,111,……}
Language:- Language is set of all string taken from ∑*
- So it is the subset of ∑*
- It is denoted by L
- There are two types of languages
- E.g.1: If L1={ Set of strings of length 2 } then { 00,01,10,11 } over the alphabet ∑={0,1}
- E.g.2: If L2={ Set of strings of length 3} then{ 000,001,010,011,100,101,110,111} over the alphabet ∑={0,1}
- E.g.1: If L3={ Set of strings of length which starts with 0 } then { 0,00,01,000,001, 010, 011,0000,………} over the alphabet ∑={0,1}
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