研究带停留时间的系统状态转移机制，给出可实现性的判定与构造方法。
Destination-Labeled Self-Looping Systems with Dwell: Intrinsic Characterization, Realization Cost, and Recognition
- 提出带停留约束的自循环系统建模框架，通过相位扩展实现状态记忆。
- 证明任意满足停留要求的确定性实现至少需总停留时间之和的控制状态数。
- 给出基于可见图的快速识别与重构算法，适用于工业控制系统设计。
研究一类有限状态符号控制器，其可见转移关系预先固定，且每个可见状态具有最小停留时间要求。该模型称为带停留的终点标记自循环系统（DLSL系统），记录可见图与局部决策映射；停留记忆仅在相位扩展后显现。核心问题是：一旦施加停留约束，当前可见状态不再决定是否允许离开。这引出逆问题：哪些确定性转换器可作为固定可见图上DLSL系统的相位扩展实现？我们证明答案正是纤维线性图保持转换器类。在自然可达性与可实现出发假设下，同一可见图上的等价可达实现彼此同构；特别地，可见转换唯一确定停留向量与局部决策映射。我们还证明，任何保持图结构并强制停留值$(d_i)$的确定性实现至少需要$ sum_i d_i$个控制状态。最后，给出$O(|Q||Ω|)$复杂度的识别与重构算法，并将分析扩展至边进入变体，其中转移可进入后继纤维的内部阶段。
原文摘要 · Abstract (English)
We study a finite-state symbolic controller for systems in which the admissible visible transitions are fixed in advance and each visible state carries a minimum dwell requirement. The resulting model, which we call a destination-labeled self-looping system with dwell (DLSL system), records the visible graph together with local decision maps; dwell memory appears only after phase expansion. The main structural issue is that, once dwell is imposed, the current visible state no longer determines whether a departure is allowed. This leads to the converse problem: which deterministic transducers arise as phase-expanded realizations of DLSL systems over a fixed visible graph? We show that the answer is exactly the class of fiber-linear graph-respecting transducers. Under natural reachability and realizable-departure assumptions, equivalent accessible realizations over the same visible graph are isomorphic; in particular, the visible transduction determines the dwell vector and the local decision maps. We also prove that any graph-preserving deterministic realization enforcing dwell values $(d_i)$ requires exactly $\sum_i d_i$ control states. Finally, we give an $O(|Q||Ω|)$ recognition and reconstruction procedure, and extend the analysis to an edge-entry variant in which transitions may enter interior phases of successor fibers.
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