Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
A fast mutual exclusion algorithm
ACM Transactions on Computer Systems (TOCS)
Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Symbolic model checking: an approach to the state explosion problem
Symbolic model checking: an approach to the state explosion problem
Formal hardware verification methods: a survey
Formal Methods in System Design - Special issue on computer-aided verification: general methods
BDD variable ordering for interacting finite state machines
DAC '94 Proceedings of the 31st annual Design Automation Conference
Workshop on Hardware Specification, Verification and Synthesis: Mathematical Aspects
Specification and verification of concurrent systems in CESAR
Proceedings of the 5th Colloquium on International Symposium on Programming
Generating BDDs for Symbolic Model Checking in CCS
CAV '91 Proceedings of the 3rd International Workshop on Computer Aided Verification
Hierarchical Representations of Discrete Functions, with Application to Model Checking
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic
Logic of Programs, Workshop
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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.