Finite-state machines, a simple class of finite Petri nets, were equipped in [16] with an efficiently decidable, truly-concurrent, bisimulation-based, behavioral equivalence, called team equivalence, which conservatively extends classic bisimulation equivalence on labeled transition systems and which is checked in a distributed manner. This paper addresses the problem of defining variants of this equivalence which are insensitive to silent moves. We define (rooted) weak team equivalence and (rooted) branching team equivalence as natural transposition to finite-state machines of Milner's weak bisimilarity [25] and van Glabbeek and Weijland's branching bisimilarity [12] on labeled transition systems. The process algebra CFM [15] is expressive enough to represent all and only the finite-state machines, up to net isomorphism. Here we first prove that the rooted versions of these equivalences are congruences for the operators of CFM, then we show some algebraic properties, and, finally, we provide finite, sound and complete, axiomatizations for them.

有限状态机是一类简单的有限Petri网，在[16]中配备了可有效判定的，真正并发的，基于双仿真的行为等效性，称为团队等效性，它保守地将经典的双仿真等效性扩展到带标记的过渡系统上，并且以分布式方式检查。本文解决了定义等价变量的问题，这些变量对静默动作不敏感。我们将（有根的）弱团队等价和（有根的）分支团队等价定义为米尔纳的弱双相似性[25]和范格拉贝克和魏兰德的分支双相似性[12]的有限状态机的自然换位。过程代数CFM [15]具有足够的表现力，可以表示所有有限状态机，甚至只能表示净同构。