Logics and automata models for languages over infinite alphabets, such as Freeze LTL and register automata, respectively, serve the verification of processes or documents with data. They relate tightly to formalisms over nominal sets, where names play the role of data. For example, regular nondeterministic nominal automata (RNNA) are equivalent to a subclass of the standard register automata model, characterized by a lossiness condition referred to as name dropping. This subclass generally enjoys better computational properties than the full class of register automata, for which, e.g., inclusion checking is undecidable. Similarly, satisfiability in full freeze LTL is undecidable, and decidable but not primitive recursive if the number of registers is limited to at most one. In the present paper, we introduce a name-dropping variant bar-muTL of Freeze LTL for finite words over an infinite alphabet. We show by reduction to extended regular nondeterministic nominal automata (ERNNA) that even with unboundedly many registers, model checking for bar-muTL over RNNA is elementary, in fact in ExpSpace, more precisely in parametrized PSpace, effectively with the number of registers as the parameter.

中文翻译：

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利用冻结定量利用 LTL

无限字母表上的语言的逻辑和自动机模型，例如 Freeze LTL 和寄存器自动机，分别用于验证流程或带有数据的文档。它们与名义集上的形式主义紧密相关，其中名称扮演数据的角色。例如，常规非确定性名义自动机 (RNNA) 相当于标准寄存器自动机模型的一个子类，其特征在于称为名称丢弃的有损条件。这个子类通常比完整的寄存器自动机类具有更好的计算特性，例如，包含检查是不可判定的。类似地，完全冻结 LTL 中的可满足性是不可判定的，如果寄存器的数量最多为 1，则可判定但不是原始递归。在本文中，我们为无限字母表上的有限单词引入了 Freeze LTL 的名称删除变体 bar-muTL。我们通过归约到扩展的常规非确定性名义自动机 (ERNNA) 表明，即使有无限多的寄存器，RNNA 上的 bar-muTL 的模型检查也是基本的，实际上在 ExpSpace 中，更准确地说是在参数化 PSpace 中，有效地将寄存器的数量作为范围。