Problem A: Given a deterministic one-counter automaton (a pushdown automaton with one stack alphabet) \(A\) and a nondeterministic one-counter net (a one-counter automaton with no zero-tests) \(N\), decide if the language recognised by $A$ is the same as the language recognised by \(N\).
Decidability of A is open. This is related to the open question of decidability for the following problem, which is relatively more well-known.
Problem B: Given a deterministic one-counter net \(D\) and a nondeterministic one-counter net \(N\), decide if the language recognised by \(D\) is the same as the language recognised by \(N\).