Hidden Markov models are foundational for sequential inference, but their Markovian assumption fails under pathwise constraints such as precedence requirements, visitation cardinalities, or monotonic state progression, which induce long-range dependencies that invalidate standard dynamic programming algorithms. To deal with this, we present Controller-Augmented Hidden Markov Models (CHMMs), a framework that compiles each constraint into a finite-state controller tracking the minimal sufficient history, after which standard forward--backward and Viterbi recursions on the augmented chain compute exact constrained posteriors and maximum a posteriori paths in both discrete and continuous time, the latter through uniformization. We establish four theoretical guarantees: exactness of constrained inference, monotone ascent of constrained EM, inference complexity linear in the controller cardinality, and a total-variation bound under constraint misspecification. A catalog of controller encodings covering 11 constraint families across the ordering, visitation, path, and temporal categories operationalizes the framework. Empirically, we evaluate CHMMs against 6 alternative decoders on 3 real-world sequence-labeling tasks of substantively different character: gene-structure decoding in \emph{Drosophila melanogaster}, free-living activity recognition in CASAS smart-home environments, and protocol-defined human activity recognition from wearable sensors. The results reveal a clean local-versus-cumulative dichotomy in which controller augmentation is uniquely able to recover globally feasible trajectories on cumulative-constraint regimes, whilst simpler decoders are matched in validity on locally-dominated regimes. Together, theory and experiment characterize when exact controller augmentation is necessary and when simpler approaches suffice.

翻译：隐马尔可夫模型是序列推断的基础，但其马尔可夫假设在面对路径级约束（如优先级要求、访问基数或单调状态演进）时失效，这些约束会引发长程依赖性，使得标准动态规划算法不再适用。为解决此问题，我们提出控制器增强隐马尔可夫模型（CHMMs），该框架将每个约束编译为一个追踪充分最小历史的有限状态控制器，随后在增强链上应用标准的前向-后向和维特比递归，即可精确计算离散和连续时间（后者通过均匀化实现）下的约束后验及最大后验路径。我们建立了四项理论保证：约束推断的精确性、约束EM的单调递增性、推断复杂度随控制器基数线性增长、以及约束错误设定下的全变差上界。通过涵盖排序、访问、路径和时间四大类别的11种约束族的控制器编码目录，实现了该框架的操作化。实验部分，我们在三个具有实质差异的真实序列标注任务上，将CHMMs与六种替代解码器进行对比评估：果蝇基因结构解码、CASAS智能家居环境中的自由活动识别、以及基于可穿戴传感器的协议定义人类活动识别。结果显示出一个清晰的局部-累积二分法：在累积约束模式下，控制器增强是唯一能够恢复全局可行轨迹的方法，而在局部主导模式下，简单解码器已能达成有效性。理论与实验共同刻画了何时必须使用精确控制器增强，以及何时简单方法即可满足需求。