# Is a k counter automata a special kind of PDA?

I understand that a 1 counter automata is a special kind of PDA where the stack alphabet consists of one symbol (ignoring the fixed bottom symbol) but what about 2 counter automata? Is it a special kind of PDA where the stack alphabet consists of two symbols? Can we generalize like so: a k-counter automata is a PDA with k many symbols in the stack alphabet where k>0?

• Well, to be precise, a single machine with $k$ pushdowns attached. As we reach $\mathrm{RE}$ already for two pushdowns (or two counters) it suffices to have only two of them (rather than $k$). Feb 16 '15 at 10:46