Timed state space exploration using POSETs

This paper presents a new timing analysis algorithm for efficient state space exploration during the synthesis of timed circuits or the verification of timed systems. The source of the computational complexity in the synthesis or verification of a timed system is in finding the reachable timed state space. We introduce a new algorithm which utilizes geometric regions to represent the timed state space and partially ordered sets (POSET's) to minimize the number of regions necessary. This algorithm operates on specifications sufficiently general to describe practical circuits, as well as other timed systems. The algorithm is applied to several examples showing significant improvement in runtime and memory usage.