Limits for automatic verification of finite-state concurrent systems
Information Processing Letters
Reasoning about networks with many identical finite-state processes
PODC '86 Proceedings of the fifth annual ACM symposium on Principles of distributed computing
Algorithms for scalable synchronization on shared-memory multiprocessors
ACM Transactions on Computer Systems (TOCS)
Reasoning about systems with many processes
Journal of the ACM (JACM)
Automatic verification of parameterized linear networks of processes
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Verifying parameterized networks
ACM Transactions on Programming Languages and Systems (TOPLAS)
ACM Transactions on Programming Languages and Systems (TOPLAS)
A new solution of Dijkstra's concurrent programming problem
Communications of the ACM
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Verifying Networks of Timed Processes (Extended Abstract)
TACAS '98 Proceedings of the 4th International Conference on Tools and Algorithms for Construction and Analysis of Systems
Beyond Parameterized Verification
TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Symbolic Model Checking with Rich ssertional Languages
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Liveness with (0, 1, infty)-Counter Abstraction
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Reducing Model Checking of the Many to the Few
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
On Model Checking for Non-Deterministic Infinite-State Systems
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Higher-Order and Symbolic Computation
FCT '07 Proceedings of the 16th international symposium on Fundamentals of Computation Theory
A generic framework for reasoning about dynamic networks of infinite-state processes
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Parameterized verification of infinite-state processes with global conditions
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Environment abstraction for parameterized verification
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Model-Checking parameterized concurrent programs using linear interfaces
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
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We present a framework for verifying safety properties of parameterized systems. Our framework is based on a combination of Abstract Interpretation and a backward-reachability algorithm. A parameterized system is a family of systems in which n processes execute the same program concurrently. The problem of parameterized verification is to decide whether for all values of n the system with n processes is correct. Despite well-known difficulties in analyzing such systems, they are of significant interest as they can describe a wide range of protocols from mutual-exclusion to transactional memory. We assume that neither the number of processes nor their statespaces are bounded a priori. Hence, each process may be infinte-state . Our key contribution is an abstract domain in which each element (a) represents the lower bound on the number of processes at a control location and (b) employs a numeric abstract domain to capture arithmetic relations between variables of the processes. We also provide an extrapolation operator for the domain to guarantee sound termination of the backward-reachability algorithm. Our abstract domain is generic enough to be instantiated by different well-known numeric abstract domains such as octagons and polyhedra. This makes the framework applicable to a wide range of parameterized systems.