Abstract
Most decidability results concerning well-structured transition systems apply to the finitely branching variant. Yet some models (inserting automata, ω-Petri nets, ...) are naturally infinitely branching. Here we develop tools to handle infinitely branching WSTS by exploiting the crucial property that in the (ideal) completion of a well-quasi-ordered set, downward-closed sets are finite unions of ideals. Then, using these tools, we derive decidability results and we delineate the undecidability frontier in the case of the termination, the control-state maintainability and the coverability problems. Coverability and boundedness under new effectivity conditions are shown decidable.
Supported by the French Agence Nationale de la Recherche, REACHARD (grant ANR-11-BS02-001), by the Fonds québécois de la recherche sur la nature et les technologies, by the Natural Sciences and Engineering Research Council of Canada and by the “Chaire DIGITEO, ENS Cachan - École Polytechnique”.
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Keywords
- Coverability Problem
- Decidability Result
- Forward Algorithm
- Broadcast Protocol
- Graph Transformation System
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Blondin, M., Finkel, A., McKenzie, P. (2014). Handling Infinitely Branching WSTS. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43951-7_2
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