Regular Separability of One Counter Automata

The regular separability problem asks, for two given languages, if there existsa regular language including one of them but disjoint from the other. Our main result isdecidability, andPSpace-completeness, of the regular separability problem for languages ofone counter automata without zero tests (also known as one counter nets). This contrastswith undecidability of the regularity problem for one counter nets, and with undecidabilityof the regular separability problem for one counter automata, which is our second result.