## 1 Introduction
Due to possessing premature feedback safety property, the proposed algorithm always executes as per its specification without premature feedback and is able to implement propagation reliability with exactly once semantics. The propagation reliability and propagation 1-safety decide the messages received by system processes. Since the 1-propagation safety property guarantees that no spurious message generated due to arbitrary initialization received by a process can be sent to its neighbors but cannot be forwarded further, it ensures that each process can receive at most one spurious message due to arbitrary initialization. The proposed algorithm also distinguishes between spurious messages and those sent by a legitimate source. Our algorithm ensures that the receipt of a spurious message is possible only once in the execution of the first enabled action of the algorithm and a message from a legitimate source cannot be received in the execution of the first enabled action by the process. Therefore, the message received after the execution of the first message receipt action by a process is always a message received from a legitimate source. This facilitates the receipt of only those messages sent by legitimate sources, implementing propagation safety. That is, a process receives at most one spurious message due to arbitrary initialization, followed by exactly one message from a legitimate source. The ability of our proposed algorithm to start in an arbitrary initial system configuration allows the algorithm to start without any reset or initialization, which in turn allows the algorithm to make progress before another phase (initialization or reset) is completed. The same allows transient faults to perturb the states of the processes that the broadcast has not reached yet. In contrast, a broadcast algorithm that requires initialization may not work when the initialized processes are perturbed by transient faults. As system sizes (number of processes) increase, the likelihood of transient faults also increases, limiting the scalability of broadcast algorithms that require initialization, whereas our proposed algorithm works even if the processes that the broadcast did not reach yet are perturbed by transient faults, making it more scalable compared to their counterparts requiring initialization. The provisions of our proposed algorithm can be facilitated by a broadcast that may fail to provide propagation reliability in its first attempt while violating the exactly once semantics. To handle the failure of the broadcast, separate mechanisms of failure detection and rebroadcast elimination of multiple message receipts are needed. Clearly, the ad hoc nature of such a protocol increases its complexity and the cost of the broadcast compared to our proposed algorithm, which inherently provides all the properties without combining separate mechanisms. In addition, due to their complexity and possible interferences among the mechanisms, such protocols become more error-prone. The proposed algorithm can be used in various real-world applications that require reliable and safe broadcast, including IoT networks [10], smart homes [11], and autonomous drones [12]. The algorithm can also be used in fields requiring strong security and isolation guarantees, such as smart cities [13], smart grid systems [14], cloud virtualization layers to ensure data security and isolation [15], and blockchains to guarantee secure data transmissions [16]. The rest of the paper is organized into five more sections. Section 2 provides the necessary preliminaries to establish a solid foundation of knowledge. In Section 3, the computational model employed in the paper is presented. Section 4 focuses on the algorithm, including its specifications, underlying principles and detailed explanation. Section 5 offers proof of the correctness of the algorithm. Finally, the paper concludes in Section 6, summarizing the key findings, drawing conclusions, and providing final remarks.