Multi-layer networks are networks in which several protocols may coexist at different layers. The Pseudo-Wire architecture provides encapsulation and decapsulation functions of protocols over Packet-Switched Networks. In a multi-domain context, computing a path to support end-to-end services requires the consideration of encapsulation and decapsulation capabilities. It appears that graph models are not expressive enough to tackle this problem. In this paper, we propose a new model of heterogeneous networks using Automata Theory. A network is modeled as a Push-Down Automaton (PDA) which is able to capture the encapsulation and decapsulation capabilities, the PDA stack corresponding to the stack of encapsulated protocols. We provide polynomial algorithms that compute the shortest path either in hops or in the number of encapsulations and decapsulations along the inter-domain path, the later reducing manual configurations and possible loops in the path.
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