How can a new process be initiated that is not a successor of the original spawning process?

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One way to initiate a new process that is not a successor of the original spawning process is through a "fork and exec" operation. This involves creating a new process by duplicating the current process through the fork() system call, and then using the exec() system call to replace the code and data of the new process with a different executable file.

Another way is to use a process scheduling or job control system, such as a daemon process or a batch job. These processes are typically started independently, without a direct relationship to the original spawning process.