This paper deals with computation of parallel degree, PARAdeg, for (dataflow) program nets with SWITCH-nodes. Ge et al. have given the definition of PARAdeg and an algorithm of computing PARAdeg for program nets with no SWITCH-nodes. However, for program nets with SWITCH-nodes, any algorithm of computing PARAdeg has not been proposed. We first show that it is intractable to compute PARAdeg for program nets with SWITCH-nodes. To do this, we define a subclass of program nets with SWITCH-nodes, named structured program nets, and then show that the decision problem related to compute PARAdeg for acyclic structured program nets is NP-complete. Next, we give a heuristic algorithm to compute PARAdeg for acyclic structured program nets. Finally, we do experiments to evaluate our heuristic algorithm for 200 acyclic structured program nets. We can say that the heuristic algorithm is reasonable, because its accuracy is more than 96% and the computation time can be greatly reduced.

PARAdeg has been defined to try to measure parallelism inherent in a program net. Studies on computation of PARAdeg have been done, but the quantitative evaluation, on how much PARAdeg fits parallelism of program nets, has not been studied. In this paper, we do the evaluation by applying genetic algorithm to measure firing completion times when PARAdeg processors, and less and more processors are provided for 400 program nets. Our experimental results show that the firing completion times decrease rapidly with increase of processors till PARAdeg and slowly when processors are increased to more than PARAdeg, which implies PARAdeg is a reasonable standard to measure parallelism of program nets.