Traversability, Reconfiguration, and Reachability in the Gadget Framework
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453_2023_Article_1140.pdf
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1.07 MB
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ea453d152630763eefe29c6b1f263d8c
Author(s)
Ani, Joshua
Demaine, Erik D.
Diomidov, Yevhenii
Hendrickson, Dylan
Lynch, Jayson
Date Issued
July 5, 2023
Publisher
Springer US
Citation
Ani, Joshua, Demaine, Erik D., Diomidov, Yevhenii, Hendrickson, Dylan and Lynch, Jayson. 2023. "Traversability, Reconfiguration, and Reachability in the Gadget Framework."
Version
Final published version
Abstract
Abstract
Consider an agent traversing a graph of “gadgets”, where each gadget has local state that changes with each traversal by the agent according to specified rules. Prior work has studied the computational complexity of deciding whether the agent can reach a specified location, a problem we call reachability. This paper introduces new goals for the agent, aiming to characterize when the computational complexity of these problems is the same or differs from that of reachability. First we characterize the complexity of universal traversal—where the goal is to traverse every gadget at least once—for DAG gadgets (partially), one-state gadgets, and reversible deterministic gadgets. Then we study the complexity of reconfiguration—where the goal is to bring the system of gadgets to a specified state. We prove many cases PSPACE-complete, and show in some cases that reconfiguration is strictly harder than reachability, while in other cases, reachability is strictly harder than reconfiguration.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s00453-023-01140-0
