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<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cnybbxuptncftdgxtodn5edz7m" style="color: black;">2009 24th Annual IEEE Symposium on Logic In Computer Science</a>
One-counter processes are pushdown systems over a singleton stack alphabet (plus a stack-bottom symbol). We study the complexity of two closely related verification problems over one-counter processes: model checking with the temporal logic EF, where formulas are given as directed acyclic graphs, and weak bisimilarity checking against finite systems. We show that both problems are P NP -complete. This is achieved by establishing a close correspondence with the membership problem for a natural<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/lics.2009.37">doi:10.1109/lics.2009.37</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/lics/GollerMT09.html">dblp:conf/lics/GollerMT09</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lbjn7wfqj5ahtj4jydadq3wbge">fatcat:lbjn7wfqj5ahtj4jydadq3wbge</a> </span>
more »... agment of Presburger Arithmetic, which we show to be P NP -complete. This fragment is also a suitable representation for the global versions of the problems. We also show that there already exists a fixed EF formula (resp. a fixed finite system) such that model checking (resp. weak bisimulation) over one-counter processes is hard for P NP [log] . However, the complexity drops to P if the onecounter process is fixed.
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