Thinking outside the box is useless NFA = FNFA

Maxence Ponsardin; Ville Salo

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arXiv · 2608.14111

Thinking outside the box is useless NFA = FNFA

Maxence Ponsardin·Ville Salo

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Abstract

We study picture-walking automata, namely finite-state automata that accept higher-dimensional parallelotope-/tensor-shaped pictures and are allowed to move in all directions depending on their current state and the currently read symbol. It is a long-standing open problem whether the nondeterministic such automata become stronger if automata are allowed to exit the picture. In this paper, we resolve the problem in full generality: NFA = FNFA, for pictures of any dimension.

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Maxence Ponsardin, Ville Salo. 2026-08-14. Thinking outside the box is useless NFA = FNFA. https://arxiv.org/abs/2608.14111

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