Abstract
We study the expressivity of Jumping Automata on Graphs (jags), an idealised model of computation with logarithmic space. jags operate on graphs by using finite control and a constant number of pebbles. In this paper we revisit the proof of Cook & Rackoff that jags cannot decide s-t-reachability in undirected graphs. Cook & Rackoff prove this result by constructing, for any given jag, a finite graph that cannot be traversed exhaustively by the jag. We generalise this result from the graphs constructed by Cook & Rackoff to a general class of group action graphs. We establish a bound on the number of nodes that a jag can visit on such action graphs. This generalisation allows us to strengthen the result of Cook & Rackoff to the existence of a graph of small degree whose diameter (rather than its number of nodes) is larger than the number of nodes the jag can visit. The main result has been formalised in the theorem prover Coq, using Gonthier’s tactic language SSReflect.
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© 2008 Springer-Verlag Berlin Heidelberg
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Schöpp, U. (2008). A Formalised Lower Bound on Undirected Graph Reachability. In: Cervesato, I., Veith, H., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2008. Lecture Notes in Computer Science(), vol 5330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89439-1_43
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DOI: https://doi.org/10.1007/978-3-540-89439-1_43
Publisher Name: Springer, Berlin, Heidelberg
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