The class of known constraint automata for which the constrained synchronization problem is in NP all admit a special form. In this work, we take a closer look at them. We characterize a wider class of constraint automata that give constrained synchronization problems in NP, which encompasses all known problems in NP. We call these automata polycyclic automata. The corresponding language class of polycyclic languages is introduced. We show various characterizations and closure properties for this new language class. We then give a criterion for NP-completeness and a criterion for polynomial time solvability for polycyclic constraint languages.

中文翻译：

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NP中一类有约束的同步问题

NP 中约束同步问题所在的已知约束自动机类都具有特殊形式。在这项工作中，我们将仔细研究它们。我们描述了更广泛的一类约束自动机，它们给出了 NP 中的约束同步问题，其中包含 NP 中的所有已知问题。我们称这些自动机为多环自动机。介绍了相应的多环语言语言类。我们展示了这个新语言类的各种特征和闭包属性。然后，我们给出了多环约束语言的 NP 完整性标准和多项式时间可解性的标准。