Re: Using the RM for ADTs
Date: Thu, 9 Jul 2009 19:26:53 -0700 (PDT)
Message-ID: <f2c89a8c-4551-4ec3-aa6e-720606808d6a_at_b25g2000prb.googlegroups.com>
On Jul 9, 9:16 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:
>
> I wasn't denying that there is symmetry, nor that it poses problems for
> identification. What I'm arguing is that despite the symmetry, there are
> still 8 nodes and 12 resistors in the cube example, which means that there
> must be a means to distinguish between the nodes and the resistors, for
> things that are indistinguishable are the same thing: that is the essence of
> identity. The nodes and components in a circuit template can be thought of
> as verticies and hyperedges in a connected hypergraph. Certainly each
> vertex can be distinguished from all other verticies and each hyperedge can
> be distinguished from all other hyperedges in the same hypergraph, can't
> they?
Ok, I understand what you're saying now.
S2: The set of equivalence classes over S1 according to the
equivalence relation defined by isomorphism
It turns out that it is difficult to represent elements of S2 other
than by using some arbitrary representative taken from S1. That is
why abstract identifiers necessarily appear in the model.
All nodes and components have unique identity in an element of S1.
However this doesn't apply to an element of S2 when there is self
symmetry in the sense of a nontrivial automorphism.
BTW I find it very interesting that the graph isomorphism problem is NP but has not yet been proven P nor NPC. In fact it is suspected that it is neither! Received on Fri Jul 10 2009 - 04:26:53 CEST