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The Recursive Arrival Problem

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arxiv 2310.01004 v1 pith:NZFV44W3 submitted 2023-10-02 cs.CC

Thomas Webster (University of Edinburgh) This is my paper · ORCID
classification cs.CC
keywords arrivalrecursiveproblemallowsbest-knowncallcalledcomplexity
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We study an extension of the Arrival problem, called Recursive Arrival, inspired by Recursive State Machines, which allows for a family of switching graphs that can call each other in a recursive way. We study the computational complexity of deciding whether a Recursive Arrival instance terminates at a given target vertex. We show this problem is contained in NP \cap coNP, and we show that a search version of the problem lies in UEOPL, and hence in EOPL = PLS \cap PPAD. Furthermore, we show P-hardness of the Recursive Arrival decision problem. By contrast, the current best-known hardness result for Arrival is PL-hardness.

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  1. ARRIVAL: Recursive Framework & $\ell_1$-Contraction

    cs.DS 2025-02 conditional novelty 7.0 of 10

    An algorithm solves ARRIVAL in time 2^{O(k log^2 n)} on n-vertex graphs of treewidth k, and G-ARRIVAL reduces to finding approximate fixed points of l1-contractions.

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