> How large do the pointers need to be? The natural answer is that each pointer uses log nbits. However, the fact that each pointer has a distinct owner makes it possible to compress the pointers to o(log n) bits.
What if you have to debug the whole situation, such that you don't always know who is the owner of a pointer you are looking at?
> A user k can call Allocate(k) in order to get a tiny pointer p; they can dereference the tiny
pointer pby computing a function Dereference(k,p) whose value depends only on k, p, and random bits;
and they can free a tiny pointer p by calling a function Free(k,p).
That is tantamount ot saying that the pointer is not actually p but the tuple <k, p>, and so its size consists of the number of bits in k, the number of bits in p plus an indication of where the division between these bits lie: where k ends and p begins.
We can abbreviate <k, p> to p in contexts where k can be implicitly understood.
What if you have to debug the whole situation, such that you don't always know who is the owner of a pointer you are looking at?
> A user k can call Allocate(k) in order to get a tiny pointer p; they can dereference the tiny pointer pby computing a function Dereference(k,p) whose value depends only on k, p, and random bits; and they can free a tiny pointer p by calling a function Free(k,p).
That is tantamount ot saying that the pointer is not actually p but the tuple <k, p>, and so its size consists of the number of bits in k, the number of bits in p plus an indication of where the division between these bits lie: where k ends and p begins.
We can abbreviate <k, p> to p in contexts where k can be implicitly understood.