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

Abstract

Abstract-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 BGPrelated 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.

On iBGP Routing Policies

“…Deciding whether a given iBGP configuration can lead to routing instabilities is computationally hard even when no iBGP policies are applied and a single prefix is considered [24]. Nevertheless, previous work [7], [8], [25] has shown that, in the absence of iBGP policies, the intrinsic complexity of the configuration check turns out to be manageable in practice through a heuristic-based approach.…”

The (surprising) computational power of the SDN data plane

“…We are not the first to use simulationtechniques to investigate the computational power of restricted network types. Chiesa et al [5], for example, show how to implement arbitrary logical circuits using networks with routers implementing simple Border Gateway Protocol (BGP) configurations. The implication is that (in theory) BGP can solve the same problems as a Turing Machine.…”

“…Finally, Perešíni and Kostić [20] show how to simulate a Rule 110 cellular automaton in a general network model (though they note that these automaton are only "the first step towards efficiently emulating tape-bounded Turing machines"-the latter being the result we achieve in our SDN model). We adopt this same general approach of simulating a more powerful computational formalism in a restricted network, but the specific techniques we use differ from [20,5,8,10] due to the different assumptions we make concerning our network's operation and/or different goals for the simulation.…”