Journal ArticleDOI
Handling infinitely branching well-structured transition systems
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In this article, the authors 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.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 maintainability and the coverability problems. Coverability and boundedness under new effectiveness conditions are shown decidable.read more
Citations
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BookDOI
Well-Quasi Orders in Computation, Logic, Language and Reasoning. A Unifying Concept of Proof Theory, Automata Theory, Formal Languages and Descriptive Set Theory
TL;DR: The rôle played by the ideals of a wqo in its bqoness is recalled and a new presentation of known examples of wqos which fail to be bqo is given.
Book ChapterDOI
The Ideal Approach to Computing Closed Subsets in Well-Quasi-orderings
Jean Goubault-Larrecq,Simon Halfon,Prateek Karandikar,Prateek Karandikar,Prateek Karandikar,K. Narayan Kumar,K. Narayan Kumar,Philippe Schnoebelen +7 more
TL;DR: Elegant and general algorithms for handling upwards-closed and downwards-closed subsets of WQOs can be developed using the filter-based and ideal-based representation for these sets.
Book ChapterDOI
The Ideal Theory for WSTS
TL;DR: It is argued that the theory of ideals prompts a renewal of the Theory of WSTS by providing a way to define a new class of monotonic systems, the so-called Well Behaved Transition Systems, which properly contains W STS, and for which coverability is still decidable by a forward algorithm.
Journal Article
Expand, enlarge, and check: New algorithms for the coverability problem of WSTS
TL;DR: In this paper, the authors present a general algorithmic schema called Expand, Enlarge and Check from which new efficient algorithms for the coverability problem of WSTS can be constructed, which has important applications for the verification of parameterized systems and communication protocols.
Dissertation
Algorithmique et complexité des systèmes à compteurs
TL;DR: In this paper, the authors propose a verification formelle, an approche algorithmique that vise a automatiser the verification du bon fonctionnement de systemes concurrents en procedant par une abstraction vers des modeles mathematiques.
References
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Journal ArticleDOI
On Communicating Finite-State Machines
TL;DR: A model of commumcations protocols based on finite-state machines is investigated and it is determined to what extent the problem is solvable, and one approach to solving it is described.
Journal ArticleDOI
Well-structured transition systems everywhere!
Alain Finkel,Ph. Schnoebelen +1 more
TL;DR: Improved definitions of well-structured transition systems allow many examples of classical systems to be seen as instances of WSTSs and show several new results.
Proceedings ArticleDOI
General decidability theorems for infinite-state systems
TL;DR: This paper presents decidability results for a class of systems, which consist of a finite control part operating on an infinite data domain, and shows that the following properties are decidable for well-structured systems: reachability; eventuality; and simulation.
Journal ArticleDOI
Verifying programs with unreliable channels
TL;DR: The verification of a particular class of infinite-state systems, namely, systems consisting of finite-state processes that communicate via unbounded lossy FIFO channels, is considered and it is shown that several interesting verification problems are decidable by giving algorithms for verifying.
Journal ArticleDOI
Finite state description of communication protocols
TL;DR: In this article, a finite state model for the specification and validation of communication protocols is considered, and the concept of direct coupling between interactiing finite state components is used to describe a hierarchical structure of protocol layers.