**Power Of Sigma **(**Σ**)** in TOC**

**
Sigma **is set of symbols, which are always

**. It is denoted with “**

*finite***”. Example of Sigma with 4 values is given below**

__Σ__Σ = {a,0,b,k}

Where a, 0, b, k are the values of sigma.

**Formula of Powers of ‘ Σ ‘**

Power of sigma follows the formula

K^{N}

Where K tells about the total number of Sigma values and N is any positive Integer which tells about the maximum length of string.

if K=4 and N=2 then it means there are 4 sigma values i.e. Σ(a,b,c,d) and Power 2 tells every string of language may contains maximum length of 2 as given below

**Σ(a,b,c,d)**** ^{4}** =

**Σ**

^{4 }**=**

**4**

^{2}**=**16

It means there are 16 strings over Σ of length 2. i.e.{aa, bb, cc, dd, ab, ac, ad, ………} where ‘aa’ is a string of length 2.

** Examples of Power Of Sigma**

**Example 1: **Suppose there are 2 alphabets of sigma i.e. (__Σ= {a,b}__). Then power of sigma is given bellows

**Sigma with power Zero.**

**Σ**** ^{0}** = Set of all (

**Σ**

^{0 }**=**

**2**

^{0}**=**1) zero strings over Σ of length 0. {ε} // no element called

**Absalom or lamda**

**Sigma with Power 1.**

**Σ(a,b)**** ^{1}** =

**Σ**

^{1 }**=**

**2**

^{1}**=**2

It means there are only two strings over Σ of single length. i.e.{a, b} where ‘a’ is a single length

**Sigma with Power 2**

**Σ(a,b)**** ^{2}** =

**Σ**

^{2 }**=**

**2**

^{2}**=**4

It means there are only four strings over Σ of length 2. i.e.{aa, ab, ba, bb} where ‘aa’ is a double length

**Sigma with Power 3**

**Σ(a,b)**** ^{3}** =

**Σ**

^{3 }**=**

**2**

^{3}**=**8

It means there are only 8 strings over Σ of length 3. i.e. {aaa, aab, baa………bbb} where ‘ aaa’ is a triple length.

**In the same way, sigma with power 4, 5, 6 and so on.**

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