Register automata (RA) are a computational model that can handle data values by adding registers to finite automata. Recently, weighted register automata (WRA) were proposed by extending RA so that weights can be specified for transitions. In this paper, we first investigate decidability and complexity of decision problems on the weights of runs in WRA. We then propose an algorithm for the optimal run problem related to the above decision problems. For this purpose, we use a register type as an abstraction of the contents of registers, which is determined by binary relations (such as =, <, etc.) handled by WRA. Also, we introduce a subclass where both the applicability of transition rules and the weights of transitions are determined only by a register type. We present a method of transforming a given WRA satisfying the assumption to a weighted directed graph such that the optimal run of WRA and the minimum weight path of the graph correspond to each other. Lastly, we discuss the optimal run problem for weighted timed automata as an example.

寄存器自动机（RA）是一种计算模型，可以通过将寄存器添加到有限自动机来处理数据值。最近，通过扩展RA提出了加权寄存器自动机（WRA），以便可以为过渡指定权重。在本文中，我们首先研究WRA中运行权重的决策问题的可判定性和复杂性。然后，我们针对与上述决策问题相关的最优运行问题提出了一种算法。为此，我们使用寄存器类型作为寄存器内容的抽象，该类型由WRA处理的二进制关系（例如=，<等）确定。另外，我们介绍了一个子类，其中转移规则的适用性和转移权重仅由寄存器类型决定。我们提出了一种将满足假设的给定WRA转换为加权有向图的方法，以使WRA的最优运行与图的最小权重路径相互对应。最后，以加权定时自动机的最优运行问题为例。