  We re-investigate the problem of LTL model-checking for finite-state systems.
Typical solutions, like in Spin, work on the fly, reducing the problem to
Buechi emptiness. This can be done in linear time, and a variety of algorithms
with this property exist. Nonetheless, subtle design decisions can make a great
difference to their actual performance in practice, especially when used
on-the-fly. We compare a number of algorithms experimentally on a large
benchmark suite, measure their actual run-time performance, and propose
improvements. Compared with the algorithm implemented in Spin, our best
algorithm is faster by about 33 % on average. We therefore recommend that, for
on-the-fly explicit-state model checking, nested DFS should be replaced by
better solutions.
