Constraint linear-time temporal logic (CLTL) is an extension of LTL that is interpreted on sequences of valuations of variables over an infinite domain. Atomic formulas can constrain valuations over a range of positions along a sequence, with the range being bounded by a parameter depending on the formula. The satisfiability and model checking problems for CLTL have been studied before. We consider the realizability problem for CLTL. The set of variables is partitioned into two parts, with each part controlled by a player. Players take turns to choose valuations for their variables, generating a sequence of valuations. The winning condition is specified by a CLTL formula — the first player wins if the sequence of valuations satisfies the specified formula. We prove that checking whether the first player has a winning strategy in the realizability game for a given CLTL formula is undecidable in general and identify decidable fragments.

约束线性时间时序逻辑 (CLTL) 是 LTL 的扩展，它根据无限域上的变量评估序列进行解释。原子公式可以限制序列中一系列位置的评估，该范围由取决于公式的参数界定。CLTL的可满足性和模型检查问题之前已经被研究过。我们考虑 CLTL 的可实现性问题。该变量集分为两个部分，每个部分都由玩家控制。玩家轮流为他们的变量选择估值，生成一系列估值。获胜条件由 CLTL 公式指定——如果估值序列满足指定公式，则第一个玩家获胜。我们证明，对于给定的 CLTL 公式，检查第一个玩家在可实现性游戏中是否具有获胜策略通常是不可判定的，并识别可判定的片段。