  Counter systems are a well-known and powerful modeling notation for
specifying infinite-state systems. In this paper we target the problem of
checking temporal properties of counter systems. We first focus on checking
liveness properties only, and propose two semi decision techniques for these
properties. Both these techniques return a formula that encodes the set of
reachable states of a given system that satisfy a given liveness property. A
novel aspect of our techniques is that they use reachability analysis
techniques, which are well studied in the literature, as black boxes, and are
hence able to compute precise answers on a much wider class of systems than
previous approaches for the same problem. Secondly, they compute their results
by iterative expansion or contraction, and hence permit an approximate solution
to be obtained at any point. We state the formal properties of our techniques,
and also provide experimental results using standard benchmarks to show the
usefulness of our approaches. Finally, we provide a technique for checking
arbitrary CTL temporal properties, which use the liveness property checking
techniques mentioned above as black boxes.
