I have a problem in constructing a Context-free Grammar for the Language $L = \{a^mb^n : m≠n,m>0,n>0\} .$ Though I can able to construct a Pushdown Automata.
I can construct a CFG, but it accepts both $m \neq n$ and $m=n$. My CFG is:
$S \to aS/Sb/aSb/aab/abb $.
I cannot able to consturct the CFG to accept for $m \neq n$ alone.