Model checking (MC) for Halpern and Shoham's interval temporal logic HS has been recently shown to be decidable. An intriguing open question is its exact complexity for full $\mathsf{\text{HS}}$: it is at least EXPSPACE-hard, and the only known upper bound, which exploits an abstract representation of Kripke structure paths (descriptor), is non-elementary.

In this paper, we provide a uniform framework to MC for full HS and meaningful fragments of it, with a specific type of descriptor for each fragment. Then, we devise a general MC alternating algorithm, parameterized by the descriptor's type, which has a polynomially bounded number of alternations and whose running time is bounded by the length of minimal representatives of descriptors (certificates). We analyze its complexity and give tight bounds on the length of certificates. For two types of descriptor, we obtain exponential upper and lower bounds; for the other ones, we provide non-elementary lower bounds.

Halpern 和 Shoham 的区间时间逻辑HS 的模型检查 (MC)最近已被证明是可判定的。一个有趣的悬而未决的问题是它的完全复杂性$\mathsf{\text{HS}}$：它至少是EXPSPACE -hard，并且唯一已知的利用 Kripke 结构路径（描述符）的抽象表示的上限是非基本的。

在本文中，我们为完整HS及其有意义的片段提供了一个统一的 MC 框架，每个片段都有一个特定类型的描述符。然后，我们设计了一个通用的 MC 交替算法，由描述符的类型参数化，它具有多项式有界的交替数，其运行时间受描述符（证书）的最小代表长度的限制。我们分析了它的复杂性并严格限制了证书的长度。对于两种类型的描述符，我们获得指数上限和下限；对于其他的，我们提供了非基本的下界。