on the definition of "hardware" and "software"
Don Mikulecky (mikuleck@HSC.VCU.EDU)
Thu, 24 Jun 1999 15:34:20 -0400
It would seem useful at this point to let everyone see Rosen's
treatment of hardware and software and the operational way they get
defined. Remember that this is all in the context of the modeling
relation's inferential structure into which an actual natural system
or a hypothetical Turing machine has been encoded. The distinction,
being operational is based on a mapping of "inputs" A to "outputs"
B by the machine. These are assumed to be operationally definable
as a direct sum. That sum can be "partitioned" operationally for
ANY GIVEN MACHINE AS IT TAKES INPUTS TO OUTPUTS as f: A-->B
identifying certain states with f others with A and still others
with B. There can be more states in the direct sum as well which do
not fit any of the three categories defined. Now note carefully,
that the state MUST be a direct sum to fit the definition of machine
Rosen has posited. Any other device does not fit the definition.
Given that it is a direct sum it can ALWAYS be partitioned and the
critea for any given machine is operational. In Rosen's words: "It
can not be stressed too strongly that, in these considerations, the
hardware, f, and the flows it induces on software are fundamentally
different things; they encode entirely different aspects of the
natural system they model." He then describes the right hand side
of the modeling relation as follows: "....all of the STATES, (i.e.
hardware plus software) go INSIDE the box, as does the flow from
input to output. The GENERATION of that flow by the hardware is
what sits outside the box as the inferential structure.."
OK what is being discussed is a model of a Turing like machine.
All its structure is inside the box meaning it is a formal system
meant to model the abstract Turing machine. All that is outside is
the inferential structure that represents what the machine uses to
carry input to output.
Now I am going to ask someone to use what was actually said to show
where the problem is. Do not use a representation which is in terms
of direct products or other non- partitionable combinations of the
state variables. This is a machine which, by definition, has its
states constructed as direct sums. Do not use another machine with
another structure to redefine the operational characteristics of
THIS machine. Start again with the next machine and do it all over
again. I see no problem here. What am I missing?
Don Mikulecky