Traversability, Reconfiguration, and Reachability in the Gadget Framework

TL;DR

This paper analyzes the computational complexity of traversing, reconfiguring, and reaching specific states in a graph of gadgets with local states, revealing many problems are PSPACE-complete and exploring their relative difficulty.

Contribution

It provides a comprehensive complexity characterization of traversal and reconfiguration problems in the Gadget framework, including cases where reconfiguration is harder or easier than reachability.

Findings

Many traversal and reconfiguration problems are PSPACE-complete.

Reconfiguration can be strictly harder or easier than reachability depending on the case.

The paper offers a detailed complexity landscape for gadget-based systems.

Abstract

Consider an agent traversing a graph of "gadgets", each with local state that changes with each traversal by the agent. We characterize the complexity of universal traversal, where the goal is to traverse every gadget at least once, for DAG gadgets, one-state gadgets, and reversible deterministic gadgets. We also study the complexity of reconfiguration, where the goal is to bring the system of gadgets to a specified state, proving many cases PSPACE-complete, and showing in some cases that reconfiguration can be strictly harder than reachability (where the goal is for the agent to reach a specified location), while in other cases, reachability is strictly harder than reconfiguration.