Using routers to build logic circuits: How powerful is BGP?

Because of its practical relevance, the Border Gateway Protocol (BGP) has been the target of a huge research effort since more than a decade. In particular, many contributions aimed at characterizing the computational complexity of BGP-related problems. In this paper, we answer computational complexity questions by unveiling a fundamental mapping between BGP configurations and logic circuits. Namely, we describe simple networks containing routers with elementary BGP configurations that simulate logic gates, clocks, and flip-flops, and we show how to interconnect them to simulate arbitrary logic circuits. We then investigate the implications of such a mapping on the feasibility of solving BGP fundamental problems, and prove that, under realistic assumptions, BGP has the same computing power as a Turing Machine. We also investigate the impact of restrictions on the expressiveness of BGP policies and route propagation (e.g., route propagation rules in iBGP and Local Transit Policies in eBGP) and the impact of different message timing models. Finally, we show that the mapping is not limited to BGP and can be applied to generic routing protocols that use several metrics.