What are the different operations performed on strings in TOC?

A string is a finite set sequence of symbols choosen from some alphabets.

For example,

• 00011001 is a string from binary alphabet Σ={0,1}
• aabbcabcd is a string from alphabet Σ={a,b,c,d}

The different operations performed on strings are explained below −

• Concatenation.
• Substring.
• Kleen star operation.
• Reversal.

Concatenation

Concatenation is nothing but combining the two strings one after another.

Example

Let’s consider two strings −

X= Tutorials

Y= Point

The concatenation (X, Y) of two strings is −

X.Y = TutorialsPoint

Note − Concatenation of empty string with other string gives string itself.

For example, X. ε = ε.X = X

Substring

If ‘w’ is a string then ‘v’ is substring of ‘w’ if there exists string x and y such that w=xvy

‘x’ is called ‘prefix’ and y is called the suffix of w.

Example

Let’s consider w=’Theory’ is defined with prefix, x=’The’ and suffix , y=’ry’.

The substring is v=’o’, because, w=xvy and Theory= Thevry

Therefore, v=o

Kleen star operation

Let ‘w’ be a string. w’ is a set of strings obtained by applying any number of concatenations of w with itself, including empty string.

Example

a*= { ε,a,aa,aaa,………}

Reversal operation

If ‘w’ is a string, then wR is the reversal of the string in backwards.

Rules

The rules for the reversal operation are as follows −

• x=(x^R)^R
• (xz)^R= z^R.x^R

Example

A string x is defined as x= tutorial then (xR)R is tutorial. This is because,

X= tutorial

(x)R= lairotut

(xR)R= tutorial