We often speak of locality as a property of subhistories for a particular object x: “H|x is strictly serializable, but H is not”. This is a strange thing to say indeed, because the transactions in H may not meaningfully exist in H|x. What does it mean to run
[(A enq y 1) (A enq x 1)]on x alone? If we restrict ourselves to those transactions that doapply to a single object, we find that those transactions still serialize in the full history.So in a sense, locality is about the scope of legal operations. If we take single enqueue and dequeue operations over two queues x and y, the space of operations on the composite system of x and y is just the union of operations on x and those on y. Linearizability can also encompass transactions, so long as they are restricted to a single system at a time. Our single-key, multi-operation transactions still satisfied strict serializability even in the composite system. However, the space of transactions on a composite system is more than the union of transactions on each system independently. It’s their product.
Here’s the part where I pretend that of course I understand what Kyle wrote… Seriously, though, this is a very interesting read.