The BDD space complexity of different forms of concurrency

Abstract

Symbolic representations using binary decision diagrams (BDDs) are popular means to cope with extremely large state spaces. However, it may be the case that the BDD representation itself is prohibitively large. We consider the BDD representations of synchronous, asynchronous and interleaved processes with communication via shared variables and present upper bounds for their sizes. For this reason, we introduce a general representation strategy where a possible exponential growth of the BDD representation can only be due to the specifics of communication and/or write conflict resolution; it is never due to the number of processes or the concurrency discipline. Moreover, certain conditions on the communication and the write conflict resolution are postulated that lead to polynomial sized BDD representations.