While automated network verification is emerging as a critical enabler to manage large complex networks, current approaches come with a high computational complexity. This paper initiates the study of communication networks whose configurations can be verified fast, namely in polynomial time. In particular, we show that in communication networks based on prefix rewriting, which include MPLS networks, important network properties such as reachability, loop-freedom, and transparency, can be verified efficiently, even in the presence of failures. This enables a fast what-if analysis, addressing a major concern of network administrators: while configuring and testing network policies for a fully functional network is challenging, ensuring policy compliance in the face of (possibly multiple) failures, is almost impossible for human administrators. At the heart of our approach lies an interesting connection to the theory of prefix rewriting systems, a subfield of language and automata theory.

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