A temporal (constraint) language is a relational structure with a first-order definition in the rational numbers with the order. We study here the complexity of the Quantified Constraint Satisfaction Problem (QCSP) for temporal constraint languages. Our main contribution is a dichotomy for the restricted class of dually-closed temporal languages. We prove that QCSP for such a language is either solvable in polynomial time or it is hard for NP or coNP. Our result generalizes a similar dichotomy of QCSPs for equality languages, which are relational structures definable by Boolean combinations of equalities.

翻译：时间( 约束性) 语言是一种关联结构, 其定义在理性数字中按顺序顺序排列。 我们在此研究时间限制语言的量化限制满意度问题的复杂性。 我们的主要贡献是限制使用两种封闭时间语言。 我们证明这种语言的QCSP要么在多元时间可以溶解,要么对NP或CNP很难。 我们的结果将平等语言的量化限制满意度问题( QCSP) 的相似二分法概括为平等语言, 平等语言是可被布尔恩语组合确定的关系结构。