We present a novel self-stabilizing version of Mazurkiewicz enumeration algorithm [1]. The initial version is based on local rules to enumerate nodes on an anonymous network. [2] presented the first self-stabilizing version of this algorithm which tolerates transient failures with an extension of messages complexity. Our version is based on local detection and correction of transient failures. Therefore, it ensures the fault-tolerance property without adding messages or reduces the messages' number of other version. In addition, we have developed an interface based on the Visidia platform to simulate faults through a graphical user interface. The implementation of the presented algorithm in this platform shows its dynamic execution and validates its correction. The asynchronous message passing version of the presented protocol shows the transformation of distributed algorithms encoded in local computations model, as a high model, to message passing model, as a weaker model. The tr...