Parallel breadth-first BDD construction

Abstract

With the increasing complexity of protocol and circuit designs, formal verification has become an important resewch area and binary decision diagrams (BDDs) have been shown to be a powerful tool in formal verification. This paper presents a parallel algorithm for BDD construction targeted at shared memory multiprocessors and distributed shared memory systems.This algorithm focuses on improving memory access locality through specialized memory managers and partial breadth-first expansion, and on improving processor utilization through dynamic load balancing. The results on a shared memory system show speedups of over two on four processors and speedups of up to four on eight processors. The measured results clearly identify the main source of bottlenecks and point out some intereeting directions for further improvements.

Parallel disk-based computation for large, monolithic binary decision diagrams

“…In 1997, Yang and O'Hallaron [29] propose a method for parallel construction of BDDs for shared memory multiprocessors and distributed shared memory (DSM) systems based on their technique named partial breadth-first expansion, having as starting point the depth-first/breadth-first hybrid approach in [1]. Their algorithms rely on very frequent synchronization of global data structures and on exclusive access to critical sections of the code which make this approach infeasible for any distributed-memory system.…”

“…Previously, researchers have used the disks of a single node in an effort to extend the available storage of a sequential BDD package [2,21,24,25]. Researchers have also developed parallel BDD algorithms with the goal of making BDD computations run faster [11,15,19,22,28,29]. All of the work cited was performed in the 1990s, with little progress since then.…”

Solid and Physical Modeling

“…These are Acyclic Binary Decision Graphs, which may be constructed through Shannon's Expansion [Yang97]. The size (number of nodes) of RFGs may be exponential in the number n of primitives and depends on their order [Payne77].…”

Multi-threaded reachability

“…In [14], parallelized BDDs are used for reachability analysis. Verification using parallel reachability analysis has been studied in [4,5,16]. A scalable parallel reachability analysis is presented in [5].…”