I would like to know if it is possible to run a local application on a distant server using the SSH protocol?
To execute locally-installed applications using another computer's CPU and memory, you could — assuming that the processors are compatible — try this. I'm not sure how well it will work, but the theory seems sound :) You will probably need superuser access on the remote server for this to work.
Or you can just
will save the list of files named "somefile" in your home temp directory on the server.
This is, at least from my point of view, pretty experimental. I'm not sure what could go wrong, but I wouldn't try it unless a few people vouch for it. Even then I wouldn't try it on a production system. If I were doing an IT TV show, this segment would be subtitled with the words "DON'T TRY THIS AT HOME".
Definitely you'll need to have compatible processors on the two machines: if the local system is i386, the server will have to be i386 or amd64. Also, since the server's kernel is going to be doing the work, you'll only be able to run local apps which work with the version of the kernel that's running on the server. It would probably be best if they were the same version. So if both your local box and the remote server are running 32-bit Debian Squeeze, then this might work without issues.
As a further note: there may be very limited advantage to doing things this way, since any data that needs to be transferred back and forth — including both files to be processed and the applications themselves — will have to be encrypted and transferred over your remote connection. So if you are looking to do this in order to harness the superior processing power of the server, you may not gain very much in the end, and may lose some.
That depends a lot on how you define the terms you are using:
So, what shall it be?
You can not execute code on a CPU without making it available to the CPU before.
You can from one machine(machine A) request that another machine(machine B) run a program already on machine B. ssh would let you do that.
And I think you can from machine A access say an installation file from machine B, and run it on machine A, which would transfer the file into machine A's RAM. I think windows file sharing does that. (that doesn't move or copy the file by the way, no file disappears or appears anywhere in doing that. Better terminology might be that the file is copied into RAM and becomes a process, this happens any time a program is run even when local)
In theory I suppose a very cool CPU and instructions could read from RAM on another computer. You'd want over a network too. Maybe the technology is literally out there but I wouldn't know where/what.