#TOC#Hopcroft and ullman #cfg

Question

How to solve this?

Design CFG for the language {aⁱb^jc^k | i=j+k}

Answer 1

Divide it into two part

S-> aSc|S₁

S₁->aS₁b| $\epsilon$

Here first i produce as many c's as i want along with a

Second part i produce as many b's i want along with a

It also takes cares of case if i want only (a and b) or (only a and c) or none

no matter what if both b and c is $\neq$ 0 the there will be a followed by b followed by c

so first fill a and c it will  help to create an void in middle which can be filled with a and b

if still finding hard then take 2 or 3 strings in mind and design an tree structure of string it might give you an direction