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::= f:A->B, function f is a 1-1 or multi-1 mapping from set A to set B
Mapping::= Let f(a)=b, 'a' is called the input, argument or parameter of 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...descriptions
of reasoning/association/connection/projection, etc. Moreover, a function can
also be defined by a set of mappings.
Computation::= 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 to the
output (solution). Input and output are composed of fixed and finite [parts].
[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/logic.
If the [part] is discrete, it can be considered that the [part] can be
described/composed by "circuit logic". Circuit logic has the concept of
time sequence, input/output, and stable/non-stable state. Traditional
logic is less suitable for temporal propositional statements.
(Computer) Problem Statement::= Describes the input (known, conditions, etc.)
and required output data that the computer can process. 'Problems' must be
presented in a narrative, but 'problems' can be described in different ways.
Just like 'mathematical problems'-- they must eventually be converted into
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::= A command statement for basic computer [part] operations, such
as basic instructions: write read/compare branch,.. move/convert, etc. The
basic [part] operation (i.e., instruction) function is deterministic and its
object is fixed.
Algorithm::= A sequence of instructions (similar to CPU instructions) that
describes the process of completing a [part] of a certain operation step by
step (or called instruction statement, flow statement, program, or simply
algorithm). In particular, the flow statement can contain conditional
branches, which can conditionally execute or repeat instructions.
Algorithmic problem (category)::= Algorithmic problem (category) usually refers
to problems that contain substitute for an unlimited number of objects in the
problem statement (such as values/numbers, arrays, sets,.. variable-length
data, etc.).
Since the statement contains substitute for an unlimited number of objects,
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::= If a function f:A->B, has a certain number of n mappings
<x1,f(x1)>, <x2,f(x2)>,...,<xn,f(xn)> are called minmax points or regional
minmax points, so that ∀a,b∈minmax point, ∀x,a<=x<=b<=n, f(a)<=f(x)<=f(b)
or f(a)>=f(x)>=f(b) holds.
Preliminary sumarization of 'computation' for review.