Re: Discussion on tetrits motion
Dan Zuras Intervals wrote:
Subject: Re: Discussion on tetrits motion
From: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
To: "P1788" <stds-1788@xxxxxxxxxxxxxxxxx>
Subject: Discussion on tetrits motion
Date: Fri, 23 Apr 2010 15:59:16 -0500
Dan, et. al.
In your 4/17 post, for all 3-bits you included the explicit tables:
No, Nate.
Those tables were part of a discussion that
only applied to the 'domain' decoration as
I understood it at the time.
In the motion just made, you will notice
that there are no such tables. The reason
for this is that they will not apply to all
decorations.
And, as this motions says nothing about any
particular decoration, I would like to make
discussion of particular decorations the
subject of some future motion.
As I said in the cover letter.
Dan
Dan,
I'm trying to make sense of your e-mail:
-- Of course there are no tables in the motion, but the definitions
that generated the 4/17 tables are the same as the definitions in the
motion. Below I include both for a "side by side" comparison... the tables
are a consequence of these definitions.
-- I believe we need to explicitly discuss advantages or
disadvantages of the proposed definitions with regard to particular
decorations that we probably will adopt, i.e., having or not having a
particular decoration should not be the issue, but how suitable the
motion enables or inhibits the goals of various decorations would be.
Sincerely,
Nate
Dan Zuras Intervals wrote(4/23/2010):
We define for all dyadic interval functions f(xx,yy):
'thingy'True = {there exists x in xx and y in yy
such that is'thingy'(f,x,y) is True}
'thingy'False = {there exists x in xx and y in yy
such that is'thingy'(f,x,y) is False}
'thingy'Sticky =
'thingy'False(xx) \or 'thingy'Sticky(xx) \or
'thingy'False(yy) \or 'thingy'Sticky(yy)
Dan Zuras Intervals wrote (4/17/2010):
+------ 'inDomain' = {There exists x in xx & y in yy such
that (x,y) is in the domain of g(x,y)}
+---- 'outDomain' = {There exists x in xx & y in yy such
that (x,y) is NOT in the domain of g()}
+-- 'outSticky' = outDomain(xx) \or outdomain(yy) \or
outSticky(xx) \or outSticky(yy)
v v v Meaning
- - - -------
F F F No points, never was, [empty] & always has been.
F F T No points, also [empty], one operand was [empty] while
the other one was outDomain or outSticky. Looks like
this state can only be reached by a dyadic function.
I'm glad I decided to check that. :-)
F T F Completely outside the domain of this function but no
previous function had that problem. Returns [empty].
F T T Completely outside the domain of g(), also [empty],
also was outside the domain of some previous function.
T F F Completely inside the domain of g() & as well as inside
the domain of all previous functions. This is the
good state we all like to see.
T F T Completely inside the domain of g() but some previous
function was not so lucky. This is also a good state
of sorts. A domain error once happened but it hasn't
bothered g(). This may or may not be of interest to
the user but it looks like something that is good to
know.
T T F Both inside & outside the domain of g() but no previous
function suffered a domain error. Any problems are g's
fault alone. This state & the next are states you
likely start with in branch & bound methods.
T T T We have points both inside & outside the domain of g()
& had problems in the past. This is the other state
you start with on branch & bound.