Derive the string “abb” for leftmost and rightmost derivation

Problem

Let’s consider a grammar to derive “abb” string using LMD and RMD

   S->AB/ ε

   A-> aB

   B-> Sb

Solution

We have to use context free grammar.

Derivation is a sequence of production rules, which is used to get input strings.

During parsing, we have to take two decisions, which are as follows −

• We have to decide which non-terminal has to be replaced.
• We have to decide which non-terminal has to be replaced by using which production rule.

There are two options to decide which non-terminal has to be replaced with production rule −

• Leftmost derivation
• Rightmost derivation

Leftmost derivation

The input is scanned and replaced with production rules from left to right.

The given production rules are:
   S->AB/ ε
   A-> aB
   B-> Sb
Let’s derive the string “abb” using LMD
   S->AB
   ->aBB {A->aB}
   ->aSbB {B->Sb}
   ->abB {S-> ε}
   ->abSb {B->Sb}
   ->abb {S-> ε}
Which is our final string

Rightmost derivation

The input is scanned and replaced with a production rule from right to left.

The given production rules are:
   S->AB/ ε
   A-> aB
   B-> Sb
Let’s derive the string “abb” using RMD
   S -> AB
   ->ASb {B->Sb}
   ->Ab {S-> ε}
   ->aBb {A->aB}
   ->aSbb {B->Sb}
   ->abb {S-> ε}
Reached our final string