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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Preliminary sumarization of 'computation' for review.
Date: Sat, 12 Jul 2025 18:53:06 +0800
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This is my preliminary sumarization of 'computation' for review.
Quantum computing is not considered, but related commnents are also welcome=
..

The nature of computation - constructing functions The process of computing
functions Correct/clear concepts help understanding

Function::=3D f:A->B, function f is a 1-1 or multi-1 mapping from set A to =
set B

Mapping::=3D Let f(a)=3Db, 'a' is called the input, argument or parameter o=
f f, and
  the pair of a,b <a,b> is called a mapping of f.

  Mapping pairs can express many things, such as stimulus-response records,
  test-result records, input-output records, iff X then Y records...descrip=
tions
  of reasoning/association/connection/projection, etc. Moreover, a function=
 can
  also be defined by a set of mappings.

Computation::=3D The process of computing from the deterministic operation =
of
  basic parts to the overall performance. (Non-parallel) computation is
  step-by-step, deterministic operation process from the input of a model t=
o the
  output (solution). Input and output are composed of fixed and finite [par=
ts].
  [Parts] are things that can be objectively operated, usually referring to=
 text
  symbols. Each [part] has a location and value attribute.

  [Note] Computation is related to theoretical reasoning in mathematics/log=
ic.
         If the [part] is discrete, it can be considered that the [part] ca=
n be
         described/composed by "circuit logic". Circuit logic has the conce=
pt of
         time sequence, input/output, and stable/non-stable state. Traditio=
nal
         logic is less suitable for temporal propositional statements.

(Computer) Problem Statement::=3D Describes the input (known, conditions, e=
tc.)
   and required output data that the computer can process. 'Problems' must =
be
   presented in a narrative, but 'problems' can be described in different w=
ays.
   Just like 'mathematical problems'-- they must eventually be converted in=
to
   narratives that can be processed in a 'mathematical' way. So, in short, =
the
   final form of computer problem statements is the problem handled by
   algorithms.

Instructions::=3D A command statement for basic computer [part] operations,=
 such
   as basic instructions: write read/compare branch,.. move/convert, etc. T=
he
   basic [part] operation (i.e., instruction) function is deterministic and=
 its
   object is fixed.

Algorithm::=3D A sequence of instructions (similar to CPU instructions) tha=
t
   describes the process of completing a [part] of a certain operation step=
 by
   step (or called instruction statement, flow statement, program, or simpl=
y
   algorithm). In particular, the flow statement can contain conditional
   branches, which can conditionally execute or repeat instructions.

Algorithmic problem (category)::=3D Algorithmic problem (category) usually =
refers
   to problems that contain substitute for an unlimited number of objects i=
n the
   problem statement (such as values/numbers, arrays, sets,.. variable-leng=
th
   data, etc.).

  Since the statement contains substitute for an unlimited number of object=
s,
  the algorithm must use loops to repeat instructions accordingly, and must=
 use
  "pointers" or indirect addressing (or index addressing) type instructions=
 to
  achieve the ability to read and write ranges of variable as [parts] with =
fixed
  instructions.

Discrete continuity::=3D If a function f:A->B, has a certain number of n ma=
ppings
  <x1,f(x1)>, <x2,f(x2)>,...,<xn,f(xn)> are called minmax points or regiona=
l
  minmax points, so that =E2=88=80a,b=E2=88=88minmax point, =E2=88=80x,a<=
=3Dx<=3Db<=3Dn, f(a)<=3Df(x)<=3Df(b)
  or f(a)>=3Df(x)>=3Df(b) holds.