Continuous One-counter Automata.

We study the reachability problem for continuous one-counter automata, COCA for short. In such automata, transitions are guarded by upper- and lower-bound tests against the counter value. Additionally, the counter updates associated with taking transitions can be (non-deterministically) scaled down by a nonzero factor between zero and one. Our three main results are as follows: we prove (1) that the reachability problem for COCA with global upper- and lower-bound tests is in NC²; (2) that, in general, the problem is decidable in polynomial time; and (3) that it is NP-complete for COCA with parametric counter updates and bound tests. [ABSTRACT FROM AUTHOR]