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Defining language | Kleene closure | String | Sigma | Alphabet set | Easy Learning Classroom

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Defining language | Kleene closure | String | Sigma | Alphabet set | Easy Learning Classroom

* Rules defined explicitly and clearly
* No ambiguities
* Universally uniform understanding
* Lets the machine
- Interpret an input uniformly every time. i.e. always produces the same output for a particular input
- Explicitly reject invalid input


* Define alphabet set
* Define rules for forming valid words and sequences of words from Sigma
Called grammar, Can be descriptive , Can be mathematical, Can also define supporting functions e.g., length(X), reverse(x)


Strings: A string a finite sequence of symbols chosen from the alphabet.
For example: 0111100 , 123045, abbbcdeg etc.


* Set closure
* Kleene Closure (applied to )
- A set of all the strings (finite) that can be formed by the elements of  where the elements may be repeated any number of times.
- Denoted by Sigma/∑*
- Also called Kleene star.



Sigma/∑* : The set of all strings over an alphabet ∑ and called Kleene Star Closure of alphabet. So we have
Sigma/∑* = ∑0 U ∑1 U ∑2 U ∑3 U……………
Sigma/∑+ : The set of all strings over an alphabet ∑ excluding empty string, ε, and called plus operation. So we have
Sigma/∑+ = ∑1 U ∑2 U ∑3 U……………

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