Re: What is an automorphism of a database instance?

On 28 dec 2007, 06:15, Kira Yamato <kira..._at_earthlink.net> wrote:
> I need help in understanding what is an automorphism of a database instance.
>
> The following definition is from the book Relational Database Theory by
> Atzeni and De Antonellis:
>
> Definition: An automorphism of a database instance r is a partial function
>         h : D --> D
> where D is the domain of the database r such that
> 1) the partial function h is a permutation of the active domain D_r, and
> 2) when we extend its definition to tuples, relations, and database
> instances, we obtain a function on instances that is the identity on r,
> namely
>         h(r) = r.
>
> I can understand 1), but I cannot understand 2).
>
> In mathematics, an automorphism is a 1-1 mapping that preserves the
> structure of an underlying set.  For example, if in some set whose
> members x, y and z obeys
>         z = x + y,
> then we expect an automorphism f on that set to also obey
>         f(z) = f(x) + f(y).
> So, the structure of "addition" is preserved.
>
> Now, back to relational database theory, what "structure" is being
> preserved by 2)?  Can someone explain the formalization in 2) more
> carefully?

I only just saw your posting so I wondered if you still needed help with this.

• Jan Hidders