Abstract
We study the problem of strong/weak bisimilarity between processes of one-counter automata and finite-state processes. We showthat the problem of weak bisimilarity between processes of one-counter nets (which are 'weak' one-counter automata) and finite-state processes is DP-hard (in particular, it means that the problem is both NP and co-NP hard). The same technique is used to demonstrate co-NP-hardness of strong bisimilarity between processes of one-counter nets. Then we design an algorithm which decides weak bisimilarity between processes of one-counter automata and finite-state processes in time which is polynomial for most 'practical' instances, giving a characterization of all hard instances as a byproduct. Moreover, we show how to efficiently compute a rather tight bound for the time which is needed to solve a given instance. Finally, we prove that the problem of strong bisimilarity between processes of one-counter automata and finite-state processes is in P.
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