Limits for automatic verification of finite-state concurrent systems
Information Processing Letters
On the regular structure of prefix rewriting
CAAP '90 Proceedings of the fifteenth colloquium on CAAP'90
Handbook of theoretical computer science (vol. B)
String-rewriting systems
An alternative solution to a problem on self-stabilization
ACM Transactions on Programming Languages and Systems (TOPLAS)
Introduction to distributed algorithms
Introduction to distributed algorithms
Automatic verification of parameterized linear networks of processes
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Self-stabilization
An efficient automata approach to some problems on context-free grammars
Information Processing Letters
Self-stabilizing systems in spite of distributed control
Communications of the ACM
Uniform Deterministic Self-Stabilizing Ring-Orientation on Odd-Length Rings
WDAG '94 Proceedings of the 8th International Workshop on Distributed Algorithms
Termination of Linear Rewriting Systems (Preliminary Version)
Proceedings of the 8th Colloquium on Automata, Languages and Programming
Transitive Closures of Regular Relations for Verifying Infinite-State Systems
TACAS '00 Proceedings of the 6th International Conference on Tools and Algorithms for Construction and Analysis of Systems: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
Symbolic Model Checking with Rich ssertional Languages
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Verifying Systems with Infinite but Regular State Spaces
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
An Automata-Theoretic Approach to Reasoning about Infinite-State Systems
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Liveness and Acceleration in Parameterized Verification
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
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Rewrite systems over words are often used for modeling distributed algorithms over linear networks (or rings) of N processes, where N is a parameter. Here we are interested in constructing a regular set of configurations G which is unavoidable, i.e., such that any infinite derivation intersects G. We give some sufficient conditions of the rewrite system that allow us to construct an unavoidable set G using Caucal's algorithm of prefix rewriting. This construction is used to show the convergence property of distributed algorithms to closed subsets of configurations. The method is useful for proving the correctness of self-stabilizing algorithms and the liveness property of termination detection algorithms. It has been implemented, and successfully applied to several significant examples, treated in a uniform mechanical way for the first time.