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arXiv · 2409.08024

Subshifts defined by nondeterministic and alternating plane-walking automata

Benjamin Hellouin de Menibus·Pacôme Perrotin
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Abstract

Plane-walking automata were introduced by Salo & T\"orma to recognise languages of two-dimensional infinite words (subshifts), the counterpart of $4$-way finite automata for two-dimensional finite words. We extend the model to allow for nondeterminism and alternation of quantifiers. We prove that the recognised subshifts form a strict subclass of sofic subshifts, and that the classes corresponding to existential and universal nondeterminism are incomparable and both larger that the deterministic class. We define a hierarchy of subshifts recognised by plane-walking automata with alternating quantifiers, which we conjecture to be strict.

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Benjamin Hellouin de Menibus, Pacôme Perrotin. 2024-09-12. Subshifts defined by nondeterministic and alternating plane-walking automata. https://doi.org/10.4230/lipics.stacs.2025.56

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