By Roderick Bloem, Swen Jacobs, Ayrat Khalimov
Whereas the vintage version checking challenge is to choose even if a finite approach satisfies a specification, the aim of parameterized version checking is to make a decision, given finite structures M(n) parameterized by means of n in N, even if, for all n in N, the procedure M(n) satisfies a specification. during this publication we give some thought to the real case of M(n) being a concurrent process, the place the variety of replicated procedures will depend on the parameter n yet each one approach is self sufficient of n. Examples are cache coherence protocols, networks of finite-state brokers, and structures that resolve mutual exclusion or scheduling difficulties. extra examples are abstractions of structures, the place the tactics of the unique structures really depend upon the parameter.
We literature during this region has studied a wealth of computational types according to numerous synchronization and communique primitives, together with token passing, broadcast, and protected transitions. frequently, various terminology is utilized in the literature, and effects are in response to implicit assumptions. during this e-book, we introduce a computational version that unites the imperative synchronization and conversation primitives of many versions, and unveils hidden assumptions from the literature. We survey current decidability and undecidability effects, and provides a scientific view of the elemental difficulties during this intriguing examine quarter.
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Additional resources for Decidability of Parameterized Verification
Such results are often described as cutoﬀs and are typically proved by exhibiting suitable simulation relations between almost all system instances of the parameterized system and a ﬁxed system instance. 3. 1 WELL-STRUCTURED TRANSITION SYSTEMS Following the work by Abdulla et al.  and Finkel and Schnoebelen , well-structured transition systems became a popular framework for reasoning about inﬁnite-state systems and parameterized systems. We begin by recalling some required notions. A binary relation Ä on a set X is a quasi-order if it is reﬂexive and transitive.
As mentioned before, Milner’s scheduler is supposed to guarantee that all tasks are activated in a round-robin fashion, and that each task can terminate before being activated again (and only terminates after actually being activated). 2, activation of the task is represented by state label A, and termination by state label C . i /: AG Ai ! Ai ! Ci ! 5 (i)). us, standard LTL model checking in rings of size up to 5 can be used to decide the PMCP for the given parameterized speciﬁcation and implementation of Milner’s scheduler in uni-directional rings.
We can deﬁne directional pairwise rendezvous, that may restrict which of its neighbors a process is allowed to synchronize with. 2 Directional Pairwise Rendezvous. ¹Note that , , and are as before. 34 4. TOKEN-PASSING SYSTEMS To obtain directional rendezvous, we instantiate the deﬁnition of directional synchronous transition for card D f1g. v/ ! v/ . v; w/ D d . w/ ! v; w/. w 0 /. As with non-directional pairwise rendezvous, this incorporates the condition with I D fwg, and the condition is trivially satisﬁed since I 0 fwg implies jI 0 j 62 card.