In this article, we deal with the detectability problem for unambiguous weighted automata (UWAs). The problem is to determine if, after a finite number of observations, the set of possible states is reduced to a singleton. Four types of detectabilities, namely, strong detectability, detectability, strong periodic detectability, and periodic detectability are defined in terms of different requirements for current state estimation. We first construct a deterministic finite state automaton (called observer) over a weighted alphabet and prove that it can be used as the current-state estimator of the studied UWA. Finally, necessary and sufficient conditions based on the observer are proposed to verify detectabilities of a UWA.

中文翻译：

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明确加权自动机的可检测性验证


在本文中，我们处理明确加权自动机（UWA）的可检测性问题。问题是确定在有限数量的观察之后，可能的状态集是否减少为单一状态。根据当前状态估计的不同要求，定义了四种可检测性，即强可检测性、可检测性、强周期性可检测性和周期性可检测性。我们首先在加权字母表上构造一个确定性有限状态自动机（称为观察者），并证明它可以用作所研究的 UWA 的当前状态估计器。最后，提出了基于观察者的充分必要条件来验证 UWA 的可探测性。