We propose an axiomatization for weighted branching bisimulation over a weighted process algebra with positive rational weights including zero and show that this axiomatization is both sound and complete. Our proof of soundness and completeness are inspired by similar results by Milner for strong and weak bisimulation and by van Glabbeek for branching bisimulation. We also show that the claim that weighted branching bisimilarity is an equivalence relation indeed holds true. As auxiliary results, we give two alternative characterizations of weighted branching bisimulation, one in terms of weighted stuttering transitions and another in terms of a relative branching base which can be seen as a linear basis from which we can construct all weighted stuttering transitions.

中文翻译：

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加权分支互模拟的完全公理化

我们提出了加权过程代数上加权分支互模拟的公理化，其具有包括零的正有理权重，并表明这种公理化既可靠又完整。我们对稳健性和完整性的证明受到 Milner 强弱互模拟和 van Glabbeek 分支互模拟的类似结果的启发。我们还表明，加权分支双相​​似性是等价关系的说法确实成立。作为辅助结果，我们给出了加权分支互模拟的两种替代特征，一种是加权口吃转换，另一种是相对分支基，可以将其视为线性基础，我们可以从中构建所有加权口吃转换。