By Rudenskaya O.G.

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3 with the atomic formula #e ≤ c for e ∈ EG and c ∈ N, meaning the number of tokens in e is smaller than or equal to c. Next we have provided an encoding M2 of L2-formulae into multiset formulae, such that graph(m) |= F ⇐⇒ m |= M2 [F ] for every reachable marking of C k (G). This translation is a kind of quantiﬁer elimination procedure, which is possible because the graph underlying C k (G) is ﬁnite. Finally, we enriched the veriﬁcation framework with a temporal logic called μL2, which is a propositional μ-calculus where atomic propositions are formulae of L2.

Along with the paper we present ﬂashes of code. For a complete vision we refer to [6,18]. 2 Running Example: Road Assistance Scenario We use as running example a simple bike scenario (see [8]), an ecological variant of the automotive case study of Sensoria. A road assistance service platform is supported by a wireless network of ad hoc stations that are situated along a road. g. to request assistance in case of breakdowns. The graph in Figure 1 depicts a simple architecture of such a system. Each bike (®) is connected to the service access point (◦) of a station (H) which is possibly shared with other bikes.

1. The ﬁnite state gts CP Deﬁnition 4 (typed gts and derivation). A (T -typed) spo gts G (sometimes also referred to as a (graph) grammar) is a tuple T, Gs , P, π , where Gs is the (typed) start graph, P is a set of production names, and π is a function which associates a T -typed production to each name in P . We denote by Elem(G) the set VT ∪ ET ∪ P . ,n} , with G0 = Gs : in this case we write Gs ⇒∗G Gn . A T -typed graph G is reachable in G if Gs ⇒∗G G. We will consider only gtss where all productions are consuming, and derivations where matches are valid.