Biology Reference
In-Depth Information
Table 12.19 Three classes of computing
Computing
Numerical
Lexical
Molecular
1. Signs
Numbers
Words
Molecules
2. Manipulated by
Computer
Computer
Living cell
3. Logic
Crisp
Fuzzy
Crisp and fuzzy
4. Energy source
Electricity
Electricity
Chemical reactions
5. Model
Turing machine
“Zadeh” machine
Bhopalator
commented on. The concept of “computing with words (CW)” was developed by
Lotfi Zadeh in the mid-1990s by “fuzzifying” traditional crisp numerical variables
into what he called “linguistic variables” (1996a, b, 2002). In Adleman (1994) an
instance of the directed Hamiltonian path was solved by manipulating DNA
fragments in test tubes. Living cells can be considered to be the smallest molecular
computers in nature, since cells have evolved to manipulate molecular signals or
messages based on genetic instructions or rules encoded in DNA, leading to desired
outputs (Ji 1999a). In 1997, I reviewed some of the vast amount of experimental
data available in the literature concerning the phenomenon of “apoptosis” (also
called “programmed cell death”) and was led to conclude that cells have evolved to
obey the following type of instructions (Ji 1997b):
If you are in cell state X and receive signal Y, then do Z. (12.54)
The conditional instruction, Statement 12.54, is very similar to (or is an example
of) the “if-then” rule in fuzzy computing or computing with words. In this sense, the
living cell and its molecular model, the Bhopalator (Ji 1985a, b), can be viewed as
the natural “fuzzy computer.” The Turing machine is not a fuzzy computer in that its
hardware is constructed on the basis of crisp binary logic, not fuzzy logic. But the
Turing machine can be made to perform computations using fuzzy logic. The salient
features of the above three classes of computing are summarized in Table
12.19
.
(2) Each of the three classes of computing shown in Table
12.19
may be viewed
as a
category
in the mathematical sense. According to (Herrlich and Strecker 1973):
A category is a triple:
C= O
ð
;
U
;
hom
Þ
ð
12
:
55
Þ
where C is category; O is a class (or a collection) whose members are called C-objects; U:
O
u is a set-valued function, where for each C-object A, U(A) is called the underlying
set of A; and hom: O
!
u is a set-valued function, where for each pair (A, B) of
C-objects, hom(A, B) is called the set of all C-morphisms with domain A and codomain B.
O
!
It should be noted that u is the class of all sets. Classes differ from sets in that
they are immune to the logical contradiction known as Russell's paradox: Let
R
be
the set of all sets that are not members of themselves. If
R
is a member of itself, then
