By Roderick Bloem, Swen Jacobs, Ayrat Khalimov
ISBN-10: 1627057439
ISBN-13: 9781627057431
ISBN-10: 1627057447
ISBN-13: 9781627057448
Whereas the vintage version checking challenge is to choose no matter if a finite process satisfies a specification, the target of parameterized version checking is to come to a decision, given finite structures M(n) parameterized through n in N, no matter if, for all n in N, the process M(n) satisfies a specification. during this ebook we give some thought to the real case of M(n) being a concurrent method, the place the variety of replicated methods will depend on the parameter n yet every one approach is autonomous of n. Examples are cache coherence protocols, networks of finite-state brokers, and structures that clear up mutual exclusion or scheduling difficulties. additional examples are abstractions of platforms, the place the procedures of the unique structures truly rely on the parameter.
We literature during this quarter has studied a wealth of computational versions in line with numerous synchronization and verbal exchange primitives, together with token passing, broadcast, and protected transitions. usually, various terminology is utilized in the literature, and effects are in line with implicit assumptions. during this booklet, we introduce a computational version that unites the vital synchronization and conversation primitives of many types, and unveils hidden assumptions from the literature. We survey present decidability and undecidability effects, and provides a scientific view of the fundamental difficulties during this interesting examine zone.
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Additional info for Decidability of Parameterized Verification
Sample text
Is is the case if one can show, for instance, that (i) for sufficiently many components, adding an extra component to the system only adds runs that can already be simulated in the smaller system, and (ii) a run in a system instance with many components can be simulated by a run in a system with a smaller number of components. is is often possible when the connectivity-graph is “homogeneous” (like a star or a clique), see Emerson and Kahlon [2000] and German and Sistla [1992]. , Browne et al. [1988]) between tuples of processes in system instances of different size.
2 consider token-passing systems with simple token. Suzuki [1988] and Emerson and Namjoshi [1995, 2003] considered systems where the token can take multiple values. 12 [Suzuki, 1988]. Let 1-Safe be the safety fragment of 1-LTLnX. PTu ; R; 1-Safe/ is undecidable for sufficiently large T. Proof idea. (based on Emerson and Namjoshi [2003, Section 6]) e main idea is to simulate n steps of a 2CM in a ring of size n, where one process in the ring will eventually raise a flag “halt” if and only if the 2CM halts in n steps.
E control-state repeated coverability problem: input: q 2 Q. Ã; 0; ; 0/ ! t1 and ti ! tiC1 for all i 2 N . e following theorem summarizes results on Petri nets and VASS important for the exposition in this book, cf. [Esparza, 1998] for a detailed survey of this area. e control state repeated coverability problem for VASS is EXPSPACE-complete. Moreover, the problem can be solved in space which is polynomial in the number of states of the VASS and exponential in the dimension of the VASS. e reachability problem is decidable (and EXPSPACEhard).
Decidability of Parameterized Verification by Roderick Bloem, Swen Jacobs, Ayrat Khalimov
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