PDA for $L= \{w : n_a(w)+n_b(w) = 2n_c(w)\}$

Question

I'm pretty new to the PDA topic.

How do I construct an NPDA for the language $$L= \{w : n_a(w)+n_b(w) = 2n_c(w)\}.$$

I've tried all the possibilities, but I still somehow end up accepting all words.

Answer 1

The idea is to store a counter $n_a(w) + n_b(w) - 2n_c(w)$ in the stack. If this number is positive, say $x$, we want to have $x$ many P's on the stack (and nothing else). If this number is negative, say $-y$, we want to have $y$ many N's on the stack (and nothing else). Otherwise we want to have a special indicator $O$ on the stack. At the end, we check that the stack consists of $O$.

I'll let you work out the details.