The BDD Space Complexity of Different Forms of Concurrency

Issue title: Application of Concurrency to System Design

Article type: Research Article

Authors: Baldamus, Michael | Schneider, Klaus

Affiliations: Institute for Computer Design and Fault Tolerance, Universität Karlsruhe, IRF, Postfach 6980, 76128 Karlsruhe, Germany

Abstract: The automated verification of concurrent systems by model checking is often confronted with the state space explosion problem. A widely adopted method to tackle this problem is to use binary decision diagrams (BDDs) for representing systems and state spaces implicitly. However, it may be that even the system representation itself is prohibitively large. It is therefore interesting to study which factors influence the size of a BDD that represents the transition relation of a system. In this article, we consider the BDD representations of synchronous, asynchronous, and interleaved processes with communication via shared variables and present upper bounds for their sizes. To this end, we introduce a general representation strategy where catastrophic exponential growth of the BDD can only be due to the specifics of communication and/or write conflict resolution; it is neither due to the number of processes nor to the concurrency discipline. Moreover, conditions on communication and write conflict resolution are presented that are sufficient for polynomial sized BDD representations.

Keywords: Binary Decision Diagrams, Concurrency, Shared Variables

Journal: Fundamenta Informaticae, vol. 50, no. 2, pp. 111-133, 2002