an:01965394
Zbl 1044.68099
Ku??era, Anton??n
The complexity of bisimilarity-checking for one-counter processes
EN
Theor. Comput. Sci. 304, No. 1-3, 157-183 (2003).
00098480
2003
j
68Q45 68Q85
One-counter automata; One-counter nets; Bisimilarity
Summary: We study the problem of bisimilarity-checking between processes of one-counter automata and finite-state processes. We show that deciding weak bisimilarity between processes of one-counter nets (which are `restricted' one-counter automata where the counter cannot be tested for zero) and finite-state processes is \(\mathbf{DP}\)-hard. In particular, this means that the problem is both \(\mathbf{NP}\) and \(\mathbf{co-NP}\) hard. The same technique is used to demonstrate \(\mathbf{co-NP}\)-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 a large subclass of instances, giving a kind of characterization of all hard instances as a byproduct. Moreover, we show how to efficiently estimate 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 \(\mathbf P\).
Reviewer (Berlin)