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An important intrinsic property of any structured Peer-to-Peer (P2P) overlay is multi-hop paths. Understanding their structure helps to solve challenging problems related to routing performance, security, and scalability. In this paper, we introduce a mathematical Diophantine model of P2P routes. Such a route aggregates several P2P paths that messages follow. A commutative context-free grammar describes forwarding behavior of P2P nodes. Derivations in the grammar correspond to P2P routes.doi:10.1145/1364644.1364646 fatcat:hvjesmbwb5eyha62yddhkfd4wa