# Constructing PDA to accept language $L=\{a^i b^j c^k \mid k\geq \min(i,j)\}$

How can I construct a PDA which accepts the language $$\{a^i b^j c^k \mid k\geq \min(i,j)\}$$

I think about different solutions such as building a stack with two-state. one state is for $$i < j$$ and another is for $$i > j$$, But I think it doesn't work.

also, The idea of poping and pushing a and b is not good. I tried it. Can Someone give me a little hint?

• Your basic idea looks like a good starting point. Try to think of how to implement the decision whether $i<j$ or vice versa, and how you could split the cases up. May 8 at 21:48
• @nirshahar I think about this. but the idea is related to pushing a and poping b, and when I do this I lost my data for c and I can't decide on that May 8 at 21:51

Your idea to differentiate between $$i and $$i >j$$ is good.
To help you building the PDA, note that $$L = \{a^ib^jc^k | k \geq i\} \cup \{a^ib^jc^k|k\geq j\}$$.