A Formalised Lower Bound on Undirected Graph Reachability
نویسنده
چکیده
We revisit the proof of Cook & Rackoff that Jumping Automata on Graphs (JAGs) cannot decide reachability in undirected graphs. Cook & Rackoff prove this result by constructing, for any given JAG, a graph, which cannot be traversed exhaustively by the JAG. In this paper we show how this result can be abstracted and modularised, so that it can be formalised in the theorem prover Coq. We demonstrate the usefulness of the modularisation by strengthening the result of Cook & Rackoff to the existence of a graph of small degree whose diameter is larger than the number of nodes the JAG can visit.
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