Parallelising Symbolic State-Space Generators

Abstract

Symbolic state-space generators are notoriously hard to parallelise, largely due to the irregular nature of the task. Parallel languages such as Cilk, tailored to irregular problems, have been shown to offer efficient scheduling and load balancing. This paper explores whether Cilk can be used to efficiently parallelise a symbolic state-space generator on a shared-memory architecture. We parallelise the Saturation algorithm implemented in the SMART verification tool using Cilk, and compare it to a parallel implementation of the algorithm using a thread pool. Our experimental studies on a dual-processor, dual-core PC show that Cilk can improve the run-time efficiency of our parallel algorithm due to its load balancing and scheduling efficiency. We also demonstrate that this incurs a significant memory overhead due to Cilk's inability to support pipelining, and conclude by pointing to a possible future direction for parallel irregular languages to include pipelining. Research funding was provided by the EPSRC under grant no. GR/S86211/01.

Measuring and Evaluating Parallel State-Space Exploration Algorithms

“…These have been used in parallel state-space exploration algorithms to facilitate orders of magnitude improvements in time-efficiency [15,19]. We applied workstealing to parallel Saturation [8], and our results using this technique demonstrated speedups on several models including a super-linear speedup. Workstealing is based on the principle that, when one processor runs out of work to do, it steals work from another processor.…”

“…In practice, the models that we used to evaluate our parallel Saturation algorithm show a combination of these factors, with performance varying from super-linear speedups to slowdowns of over 60% [8,9]. Other parallelisations of state-space exploration algorithms also show widely varying performance of the algorithm according to the models' characteristics [15].…”

“…For example, Cilk [10], which is a library for shared-memory architectures, offers an in-built efficient load balancing and scheduling model. However, because of Cilk's restrictions on this model and its inability to deal with producer/consumer problems efficiently, our Cilk implementation of parallel Saturation encountered high memory overhead [8]. Thus, any library used to schedule and load balance a parallel state-space exploration algorithm must be able to express producer/consumer problems efficiently, but currently no library exists that is suitable for this type of problem.…”

“…For example, our experiments on parallel Saturation are put into context by the profiles in Fig. 6, where we illustrate three of our ten profiled real models, namely Robin, Kanban and FMS, which were included in our benchmark that was used in [8,9]. The models fit into the stereotypical categories shown in Fig.…”

“…We contribute the knowledge from our investigation into irregularity and subsequent overheads impacting on our parallel algorithm [8,9]. Based on this investigation we suggest an approach to evaluating parallel state-space exploration algorithms, which compliments the use of benchmarking to assess performance and the quality of parallelisation.…”