In the present paper, we introduce the backdoor set approach into the field of temporal logic for the global fragment of linear temporal logic. We study the parameterized complexity of the satisfiability problem parameterized by the size of the backdoor. We distinguish between backdoor detection and evaluation of backdoors into the fragments of Horn and Krom formulas. Here we classify the operator fragments of globally-operators for past/future/always, and the combination of them. Detection is shown to be fixed-parameter tractable whereas the complexity of evaluation behaves differently. We show that for Krom formulas the problem is paraNP-complete. For Horn formulas, the complexity is shown to be either fixed parameter tractable or paraNP-complete depending on the considered operator fragment.

中文翻译：

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线性时序逻辑的后门

在本文中，我们将后门集合方法引入到线性时间逻辑的全局片段的时间逻辑领域。我们研究了由后门大小参数化的可满足性问题的参数化复杂性。我们将后门检测和后门评估区分为 Horn 和 Krom 公式的片段。这里我们对过去/未来/总是的全局运算符的运算符片段进行分类，以及它们的组合。检测被证明是固定参数易处理的，而评估的复杂性表现不同。我们表明，对于 Krom 公式，问题是 paraNP 完全的。对于 Horn 公式，复杂性显示为固定参数易处理或 paraNP-complete，具体取决于所考虑的算子片段。