By Roderick Bloem, Swen Jacobs, Ayrat Khalimov
Whereas the vintage version checking challenge is to make your mind up no matter if a finite approach satisfies a specification, the target of parameterized version checking is to make your mind up, given finite platforms M(n) parameterized through n in N, no matter if, for all n in N, the method M(n) satisfies a specification. during this e-book we examine the $64000 case of M(n) being a concurrent approach, the place the variety of replicated strategies is determined by the parameter n yet each one strategy is self reliant 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 structures, the place the methods of the unique platforms truly rely on the parameter.
We literature during this sector has studied a wealth of computational types according to quite a few synchronization and verbal exchange primitives, together with token passing, broadcast, and protected transitions. frequently, varied terminology is utilized in the literature, and effects are in keeping with implicit assumptions. during this publication, we introduce a computational version that unites the valuable synchronization and verbal exchange primitives of many versions, and unveils hidden assumptions from the literature. We survey latest decidability and undecidability effects, and provides a scientific view of the fundamental difficulties during this fascinating learn region.
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Additional info for Decidability of Parameterized Verification
4 Milner’s Scheduler for 4 Tasks. Deadlocks. / for token-passing process templates both guarantee the absence of deadlocks for direction-unaware systems. Note that the same is not true for directionaware systems: the processes which are ready to receive might accept the token only from certain directions, which may be diﬀerent from the directions into which the process that has the token can send it. is can lead to a deadlock if all process run into states from which the only possible transition is a token-passing transition.
E coverability problem: input: ﬁnite set of states T S . output: ‘Yes’ if and only if there exist Ã 2 I and t 2 "T such that Ã ! t . e following theorem can be easily obtained from the work by Abdulla et al.  and Finkel and Schnoebelen . 3 e coverability problem is decidable for WSTSs, if the initial state set I satisﬁes one of the following conditions. 1. I is ﬁnite. 2. I is downward closed, and has a computable set membership. Proof. e proof idea is similar in both cases. C /.
One can show that for every graph G , evaluating a k-LTLnX-formula in P G amounts to a Boolean combination of the model-checking results of on the k -topologies of G . us, the k -topologies, together with the original property, give the ﬁrst part MCf i n of our decomposition. Since there are only ﬁnitely many k -topologies, and thus only ﬁnitely many Boolean formulas that combine these model checking results, one of them must be the ˚B that is the second part of the decomposition. Looking closely at the decomposition, we note that the Boolean formula ˚B depends on the quantiﬁer structure of as well as on G .