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 ∑*=∑U ∑U ∑U ∑3U…..
  •       For example over ∑= {0,1}
        ∑* ={ Ɛ,0,1,00,01,10,11, 000,001,010,011,100,101,110,111,……}
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 ∑+= ∑U ∑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
                      Finite Language: It is a finite set of string.
  • 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}
     Infinite Language: It is infinite set of string.
    • 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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