You can devise all sorts of distributed system architectures. You could for example have a synchronous system system composed of nodes organized in a ring.
There is not "one definition" of what a distributed system is. You have to define that. There are some common distributed system architectures that perhaps most of us are familiar with--asynchronous networked system, e.g. no shared memory with point-to-point communication. There are other dichotomies; though I'm not an expert in the field and am unable to succinctly define them.
As you add more "stuff" into your distributed system--people talkig about adding a memcached or whatever in other comments, you've introduce a completely different system. Maybe some sort of hybrid. And if you're interested, you can formally reason about its behavior.
Regardless, you have to define what you're talking about.
It's an interesting question to ask what is the most fundamental component of a distributed system? Could it be multiple processing nodes?
There is not "one definition" of what a distributed system is. You have to define that. There are some common distributed system architectures that perhaps most of us are familiar with--asynchronous networked system, e.g. no shared memory with point-to-point communication. There are other dichotomies; though I'm not an expert in the field and am unable to succinctly define them.
As you add more "stuff" into your distributed system--people talkig about adding a memcached or whatever in other comments, you've introduce a completely different system. Maybe some sort of hybrid. And if you're interested, you can formally reason about its behavior.
Regardless, you have to define what you're talking about.
It's an interesting question to ask what is the most fundamental component of a distributed system? Could it be multiple processing nodes?