独立语言与依赖（不满足）的见证者
Independent Languages and Witnesses of Dependence (Non-satisfaction)
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中文总结 AI 辅助
本文研究由不含补运算的正则运算定义的φ-独立语言性质，证明其与Jürgensen独立性的关系，定义并计算正则语言对应的不满足方程的见证者，同时证明该问题为PSPACE完全问题。
中文摘要 AI 辅助
我们考虑由语言方程φ(X)=∅定义的独立语言性质，其中表达式φ包含语言变量X、常量语言，以及包括转导在内的标准正则运算，但不含补运算。该性质由所有满足φ(L)=∅的语言L组成。根据φ中运算的选择，该方程定义了一大类码，包括标准变长码与检错码的组合。我们证明任何φ-独立性均为Jürgensen独立性；针对语言L，我们定义了φ(X)=∅不满足的见证者，并证明当L为正则语言时如何计算该不满足见证者；我们还讨论了该问题的复杂性，证明其判定版本为PSPACE完全问题。
英文摘要
We consider the independent language property defined by the language equation φ(X)=\emptyset, where the expression φ involves the language variable X, constant languages, and standard regular operations including transductions, but not complementation. This property consists of all languages L satisfying φ(L)=\emptyset. Depending on the choice of the operations in φ, the equation defines a broad class of codes, including combinations of standard variable-length codes and error-detecting codes. We show that any φ-independence is a Jürgensen independence, we define what a witness of non-satisfaction of φ(X)=\emptyset is, for a language L, and we show how to compute a witness of non-satisfaction when L is regular. We also discuss the complexity of the problem, showing that the decision version of the problem is PSPACE-complete.
