一句话：证明 flat freeze LTL 在单计数器自动机上的模型检测是 NEXPTIME-完全，统一一元与二进制编码。
本文研究单计数器自动机（OCA）上 freeze LTL 的模型检测问题。freeze LTL 通过 freeze 量词把运行中不同计数器值存入寄存器并比较；一般情形不可判定，因此聚焦限制 freeze 量词使用的 flat 片段。作者将问题归约到带参数化测试的 OCA（OCA(P)）可达性，并创新地用双向交替自动机模拟 OCA(P)，从而给出参数值的指数上界，进而对一元更新 OCA(P) 得到 NP 算法。作为推论，flat freeze LTL 模型检测无论计数器更新用一元还是二进制编码均为 NEXPTIME-完全；还给出单参数时钟闭合参数化时间自动机可达性属于 NEXPTIME 的替代证明。
We consider the model-checking problem for freeze LTL on one-counter automata (OCA). Freeze LTL extends LTL with the freeze quantifier, which allows one to store different counter values of a run in registers so that they can be compared with one another. As the model-checking problem is undecidable in general, we focus on the flat fragment of freeze LTL, in which the usage of the freeze quantifier is restricted. In a previous work, Lechner et al. showed that model checking for flat freeze LTL on OCA with binary encoding of counter updates is decidable and in 2NEXPTIME. In this paper, we prove that the problem is, in fact, NEXPTIME-complete no matter whether counter updates are encoded in unary or binary. Like Lechner et al., we rely on a reduction to the reachability problem in OCA with parameterized tests (OCA(P)). The new aspect is that we simulate OCA(P) by alternating two-way automata over words. This implies an exponential upper bound on the parameter values that we exploit towards an NP algorithm for reachability in OCA(P) with unary updates. We obtain our main result as a corollary. As another application, relying on a reduction by Bundala and Ouaknine, one obtains an alternative proof of the known fact that reachability in closed parametric timed automata with one parametric clock is in NEXPTIME.