由非确定性和交替平面行走自动机定义的子移位
Subshifts defined by nondeterministic and alternating plane-walking automata
AI总结：
本文扩展Salo & Törma提出的平面行走自动机模型，引入非确定性和量词交替，证明其识别的子移位是sofics子移位的严格子类，存在/全称非确定性类不可比较且大于确定性类，还定义了交替量词层次结构并推测其严格性。
摘要：
平面行走自动机由Salo & Törma提出，用于识别二维无限字（子移位）语言，是二维有限字的4向有限自动机的对应模型。我们扩展该模型以允许非确定性和量词交替。我们证明识别的子移位构成sofics子移位的严格子类，存在性和全称非确定性对应的类不可比较且均大于确定性类。我们定义了由带交替量词的平面行走自动机识别的子移位层次结构，并推测其为严格层次。
英文摘要：
Plane-walking automata were introduced by Salo & Törma 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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