  We propose two parallel state-space exploration algorithms for hybrid systems
with the goal of enhancing performance on multi-core shared memory systems. The
first is an adaption of the parallel breadth first search in the SPIN model
checker. We show that the adapted algorithm does not provide the desired load
balancing for many hybrid systems benchmarks. The second is a task parallel
algorithm based on cheaply precomputing cost of post (continuous and discrete)
operations for effective load balancing. We illustrate the task parallel
algorithm and the cost precomputation of post operators on a
support-function-based algorithm for state-space exploration. The performance
comparison of the two algorithms displays a better CPU
utilization/load-balancing of the second over the first, except for certain
cases. The algorithms are implemented in the model checker XSpeed and our
experiments show a maximum speed-up of $900\times$ on a navigation benchmark
with respect to SpaceEx LGG scenario, comparing on the basis of equal number of
post operations evaluated.
