Is it possible to pause a process, save the memory contents to a file, and then later reload the file so you can continue the program?
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Technically it is possible, but it would require saving all the system-allocated resources state too - like file descriptors for example and then restoring them. So it's a challenging task.
The easiest way to achieve what you want is to use a virtual machine like VMWare. When you pause it you actually save the whole machine state together with all programs running.