From: Mike Stay <metaweta@gmail.com>
To: categories <categories@mta.ca>
Subject: Functionally complete/universal basis for graph homomorphisms?
Date: Mon, 25 Sep 2017 22:17:30 -0600 [thread overview]
Message-ID: <E1dwrt5-0004cr-IJ@mlist.mta.ca> (raw)
The Sheffer stroke / NAND gate suffices to implement any function from
2^n -> 2. I'm looking for a similar universal basis for graph
homomorphisms from Omega^n -> Omega, where Omega is the subgraph
classifier with two vertices t, f and five edges
in:t->t, out1:t->t, out2:t->f, out3:f->t, out4:f->f.
There's obviously a finite set of operations that covers all graph
homomorphisms from Omega^n to Omega, because the set of all operations
of that form is finite. But how small can that set be? I'd be
satisfied with a formula parametric in n, but surprised if it actually
depends on n; I'd expect it to be a finite set of binary operations.
--
Mike Stay - metaweta@gmail.com
http://www.cs.auckland.ac.nz/~mike
http://reperiendi.wordpress.com
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2017-09-26 4:17 UTC|newest]
Thread overview: 9+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-09-26 4:17 Mike Stay [this message]
2017-09-26 16:49 ` Gershom B
2017-09-27 4:28 ` Patrik Eklund
2017-09-28 5:50 ` Vaughan Pratt
2017-09-30 8:18 ` Patrik Eklund
2017-09-30 18:25 ` John Baez
2017-10-02 3:58 ` Vaughan Pratt
2017-09-27 21:26 ` Mike Stay
2017-09-28 21:18 ` John Baez
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=E1dwrt5-0004cr-IJ@mlist.mta.ca \
--to=metaweta@gmail.com \
--cc=categories@mta.ca \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).