Download GRID T-EGG: A FORMAL LANGUAGE OF GRID GENBIOM

GRID UNIVERSAL GENBIOM U-EGG PROGRAMMING
Fevzi Ünlü
Yasar University, Bornova, Izmir, Turkey
e-mail: [email protected] or [email protected]
ABSTRACT
The aim of this paper is many fold: 1) A grid universal GENBIOM KBO U-egg type is studied,
designed, and introduced as a set of sentences of some formal languages, each of which is called a grid U-egg
language, nL, generated by a formal grammar, nG, all in mod n = [0, 1, 2, …, n-1}. 2). A differentiation
operator D and an integration operator I are defined on the universal GENBIOM KBO U-egg type. 3) Using nG
of nL , some token grid universal GENBIOM KBO programming form for injecting all well defined logic
functions of mod n, by an easy instant remote programming technique is studied. 4) A proper technique for
injecting all logic functions, nF, into a proper U-egg has been found for each mod n . 5) An abstract grid
programming technology has been found to manage utilization of different U-egg clusters in an harmony as a
single U-egg has been developed for realizing any CITALOG structures. The background information and
technology related to T-EGG can be found in Ünlü [1, 2, 3, 18, 19 and at all].
1 INTRODUCTION
Ünlü [1-14] studied, developed, and introduced the existence of remote programmable
a) token K-economy entity, b) token KBO-economy entity, c) token I@I-economy entity, and
d) token GENBIOM economy entity under an integrated name of (K, KBO, I@I, token
GENBIOM)-economy. Where, K stands for “Knowledge,” KBO stands for “Knowledge
Based Object,” I@I stands for “Internet at Internet,” and GENBIOM stands for “Generalized
abstract Bio-KBO type high technology dependent state Machine.” Ünlü [15 -19] studied,
developed and introduced TASIM and CITALOG. Where, TASIM stands for “Tidy
Automatic Sequential Information processing Mechanism,” and CITALOG stands for
“Compact and Integrated TAsim LOGic.” In this paper, on the bases of TASIM, CITALOG
and GENBIOM, a grid T- EGG is going to be designed, and introduced as a grid GENBIOM
economy generating TASIM relational forms.
2 GRID T-EGG’S SYNTAX FOR GENERATING GENBIOM ECONOMY
In this section a grid T-EGG will formally be studied, developed, and introduced.
2.1 GRID T-EGG SYNTAX FOR GENBIOM ECONOMY GENERATING TASIM
RELATIONAL DRESS FORMS AND GENBIOM FORMS.
Let GENBIOM be brief vocabulary used for “Generalized abstract Bio-KBO type
high technology dependent state Machine.”
Definition 1: In grid G-EGG:
(a) 1) (i.) “o” is a generalized memory dress form type. (ii) “-“is a connection-line dress
form type. (iii) “” is a nakedness dress form type. (iv) “[” is a non remote
programmable antenna dress form type which is directed to another non remote
programmable antenna dress form type “]”. Hence, “[” or “]” is a non remote
programmable antenna dress form type that is directed to each other.
2) “o-[” or “[-o” is a remote programmable antenna dress form type which is
directed to “o-]” or “]-o”. Hence, “o-[” or “[-o” or “o-]” or “]-o” is a remote
programmable antenna dress form type. Where, “o-[” = “[-o” and “o-]” = “]-o”.
3) “i[” , “]i”, “o-i[”, or“i[-o” or “o-]i” “]i-o” is an antenna indexed by technologyinterpretation index i mod n that is i  [n] = {0,1, ..., n-1}.
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4) “(” is an antenna dress form type that it behaves as “[” or “o-[” and “)” is an
antenna dress form type that it behaves as “]” or “]-o”. Where, the antenna type “(“
behaves as a transmitter-GENBIOTA while the antenna type “)” behaves as a receiverGENBIORA and vice-versa.
(b) Let G be a naked token GENBIOM entity.
1) (a) “(G” is said to be a token GENBIOM entity G which is dressed by a one-layer
antenna dress form type “(”.
(b) “0( 1( … i( … n-1( n( G ” is said to be a token GENBIOM entity G which is
dressed by an (n+1)-layers antenna dress form type “(” each of which indexed by a
technology-interpretation index i mod (n+ 1), n  N.
2) (a) “G)” is said to be a token GENBIOM entity G which is dressed by a one-layer
antenna dress form type “)”.
(b) “ G)n )n-1 … )i … )1 )0 ” is said to be a token GENBIOM entity G which is
dressed by an (n+1)-layers antenna dress form type “(” each of which is indexed by a
technology-interpretation index i mod (n+ 1), n  N.
3) (a) “(G)” is said to be a token GENBIOM entity G which is dressed by one-layer or
one pair of antenna dress form types directed to each other.
(b) “0( 1( … i( … n-1( n( G )n )n-1 … )i … )1 )0 ” is said to be a token GENBIOM entity
G which is dressed by (n + 1)-pairs or (n+1)-layers antenna dress form type “( and )” each
of which indexed by a technology-interpretation index i mod (n+ 1), n  N.
4) (a)“o-G” or “G-o” is said to be a token GENBIOM entity G which is first dressed
by a connection-line dress form type, and later it is dressed by a memory dress form type.
Where, “o-G” = “G-o”.
(b) A G dressed by a memory is called a programmable G.
(c) A G dressed by an antenna is called a communicating G.
(d) A G dressed by an antenna with a memory dress is called remote
programmable G.
5) (a)  ={(, ), (…), …, (( … (( , 0( 1( … i( … n-1( n(, ))…) …)) , )n )n-1 … )i … )1 )0 }
is called a primitive grid T-EGG dress alphabet for primitive token communicating dress
entity in a GENBIOM environment. Where, (( … (( = 0( 1( … i( … n-1( n(, ))…) …)) =
)n )n-1 … )i … )1 )0 .
(b) Let G be a token GENBIOM name, G ={G, (G, G), ((…(…((G, G))…)…)),
…, 0( 1( … i( … n-1( n(G, G)n )n-1 … )i … )1 )0 , …, ((…(…(G))…)…)), 0( 1( … i( … n-1( n(G)n
)n-1 … )i … )1 )0 } is called a primitive token GENBIOM form entity. Where,
((…(…((G))…)…)) = 0( 1( … i( … n-1( n(G)n )n-1 … )i … )1 )0 .
Definition 2 Let G be a naked GENBIOM.
(a) A primitive token GENBIOM form ((…(…((G))…)…)) or 0( 1( … i( … n-1( G )n-1
… )i … )1 )0 is called a token GENBIOM form entity in mod n. Where, n § [n] = {0, 1, 2,
…, n-1}.
(b) If G is a non terminal GENBIOM variable on mod n and C is a non terminal
GENBIOM constant in mod n, then (( …(…((G@C)@C) …) …@C) or 0( 1( … i( … n-1(
n(G@)n @C)n-1 …@C)i … @C)1 @C)0 . is called a primitive G-EGG . Where, @ is called
separating wall-operator.
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RESULTS
Result 1
a) A token GENBIOM form o-G is obtained from a non remote programmable
token GENBIOM G by injecting GENBIOM G into a GENBIOM dress form o-….
b) A token GENBIOM form G is obtained from a token GENBIOM form o-G by
sucking GENBIOM G out of GENBIOM o-G.
Hence there exist two pairs of operations in the GENBIOM economy processing.
Namely they are { +:dress forming, -:undress forming }-operations and {+:injecting into, :sucking out }-operations. They can be used in a description of GENBIOM economy
processing.
Result 2
There exist two types of alphabets in a T-EGG GENBIOM economy processing. They
are namely dressed and undressed alphabets. Each can be obtained from each other by the {
+
:dress forming, -:undress forming }-operation or {+:injecting into, -:sucking out }operation in a T-EGG GENBIOM economy processing.
Result 3
There exist two types of token GENBIOM form description entity in a GENBIOM
economy. They are namely dressed token GENBIOM form entity and undressed token
GENBIOM token entity. Each description can be obtained from other by the { +:dress
forming, -:undress forming }-operations or { +:injecting into, -:sucking out }-operations in
a T-EGG GENBIOM economy processing.
2.1 T-EGG SYNTAX FOR GENBIOM ECONOMY GENERATING TASIM
RELATIONAL GENBIOM FORMS
Any string of symbols in a token T-EGG GENBIOM economy relational form entity
generated by the following rules is said to be a token T-EGG GENBIOM relational TASIM
description entity in GA.
SYR-1 a) An undressed empty word type token GENBOM description relational form entity
“ε” is a non-communicating token T-EGG GENBIOM empty word description in a
clustered relational form entity in the naked environment of GA, while a dressed up o- ε  is
a communicating token T-EGG GENBIOM empty word description form entity in a
clustered relational form entity in a dressed up environment of GA.
b) A constant type token GENBIOM description entity “c” in sA, or ℓA, or ℓA+, or TEGG
A, or GA is a non-communicating token T-EGG GENBIOM constant word description
form entity GA, while a dressed up constant word description “o-c” in o-sA, or o-ℓA,
or o-ℓA+, or o- T-EGGA, or o- GA is a communicating token T-EGG GENBIOM word
description form entity in o- GA.
c) An undressed variable type token GENBIOM description entity “x” in sA, or ℓA, or
ℓ +
A , or T-EGGA, or GA is a non-communicating token T-EGG GENBIOM variable
description relational form entity in a naked environment of GA, while a dressed up token
GENBIOM entity o-x  in o-sA, or o-ℓA, or o-ℓA+, or o- T-EGGA, or o- GA is a
communicating token T-EGG GENBIOM constant description relational form entity in GA.
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SYR-2 Let G be an arbitrary choosen token T-EGG GENBIOM relational form in
A, or ℓA, or ℓA+ , or T-EGGA, or GA; then “ux.G” is a token T-EGG GENBIOM function
description form in GA.
SYR-3 Let 1) “@” be a separator (or a wall) operator in sA. 2) Let “(“or “)” be
GENBIOT or GENBIOR, or GENBIOM description type that it organizes directed depth
(or deepness) group-communication operators in sA, or ℓA, or ℓA+, or T-EGGA, or GA. 3) U
and T are two arbitrary token T-EGG GENBIOM descriptions in a clustered relational
form entity, then (U @ T ) is a token T-EGG GENBIOM instructional process
description form in GA. If U is T_EG GENBIOM function description form then (U @ T ) is
a token T-EGG GENBIOM instruction process description form in GA.
SYR-4 Let S be a special symbol in sA or ℓA , or ℓA+ , or T-EGGA, or GA for
representing a partial or complete substitution operator. Let G be an arbitrary token TEGG GENBIOM relational form entity that it has in its content an arbitrary Tk token TEGG GENBIOM description form entity. If Ti is a token T-EGG GENBIOM description
form entity in GA, than Ti S Tk .G is a token T-EGG GENBIOM substitution process
description form in GA.
SYR-5 Let “” be a generalized assignment operator in sA ; Let “P” be a token TEGG GENBIOM description form entity in GA. that it assumes a token T-EGG GENBIOM
description as a relational form entity value “V”. If “V” is in sA or ℓA , or ℓA+ , ℓA+ , or TEGG
A, or GA then “ P  V ” is a token T-EGG GENBIOM loading or assignment process
description form in GA .
SYR-6 5 Let “=” be reduction (or expansion) operator in sA. Let “H” and “R” be two
token T-EGG GENBIOM descriptions for some clustered relational form entities in sA or
ℓ
A , or ℓA+ , ℓA+ , or T-EGGA, or GA ; than “H = R ” is a token T-EGG GENBIOM
equivalence process description form in GA.
SYR-7 A token T-EGG GENBIOM process description in GA can only be produced
by the above six syntax rules.
s
EXAMPLES
1) ε is a token T-EGG GENBIOM empty word description in GA generated by
SYR-1a.
2) x is a token T-EGG GENBIOM variable description in GA generated by SYR-1b
3) ux.x is a token T-EGG GENBIOM function description in GA generated by SYR1c and SYR-2.
4) (ux.x @ y) is a token T-EGG GENBIOM instruction description in GA generated
by SYR-1c, SYR-2 and SYR-3.
5) xS(ux.x@y.(x@y) is a token T-EGG GENBIOM conversion process
description in generated by SYR1-3, SYR-2, SYR-3, and SYR-4.
6) x  ux.uy.x is a token T-EGG GENBIOM assignment process description in GA
generated by SYR1-3, SYR-2, and SYR-5.
7) (ux.(uy.y @ (x@x))@ uz.z) = uz.z is a token T-EGG GENBIOM instructional
process description in GA generated by SYR-1c, SYR-2, SYR3, and SYR-6.
2.2 SEMANTICS FOR GENBIOM ECONOMY GENERATING TASIM
RELATIONAL GENBIOM FORMS
Definition 2
SER-1 (a) A token T-EGG GENBIOM description relation form entity in GA is said to
be:
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1) An empty token T-EGG GENBIOM description relational form entity if it
has been produced by SYR-1a.
2) A letter token T-EGG GENBIOM description relation relational form entity
if it has been produced by SYR-1b or SYR-1.3.
3) A function token T-EGG GENBIOM description relational form entity if it
has been produced by SYR-2.
4) An instruction or instructional token T-EGG GENBIOM description
relational form entity if it has been produced by SYR-3.
5) A generalized substitution token T-EGG GENBIOM description relational
form entity if it has been produced by SYR-4.
6) A derivational equality token T-EGG GENBIOM description relational
form entity if it has been produced by SYR-5.
7) A reduction and expansion token T-EGG GENBIOM description relational
form entity if it has been produced by SYR-6.
(b) A token T-EGG GENBIOM description relational form entity in GA is a G.
Where, G stands for a “token T-EGG GENBIOM description relation form
entity” laid by TASIM.
SER-2 A derivational G is said to be:
1) A G program, if P is a string in ℓA+ and V is an instruction description
relational form type in GA produced by SYR-3.
2) A special G program of operating system, if P is a string in ℓA+ and V is an
instruction description form type G for operating system in GA produced by
SYR-3.
3) An assignment statement, if P is a string ℓA+ and V is an arbitrary G in GA
produced by SYR-3.
SER-3 An arbitrary G = {G, ‹G, G›, o-G, G-o, o-‹G, G›-o, o-‹G›, ‹G›-o, o-‹G›-o}” is
said to be a token T-EGG relational form entity. Where
1) G is a description for an arbitrary token T-EGG GENBIOM relational form
type that it has a
2) ‹G is a description for an arbitrary token T-EGG GENBIOM relational
form type that it has capacity to communicate with an eastern style
antenna..
3) G› is a description for an arbitrary token T-EGG GENBIOM relational
form type that it has capacity to communicate with a western style
antenna..
4) o-G is a description for an arbitrary remote programmable T-EGG
GENBIOM relational form type that it has capacity to be remote
programmed by some western style programming technology..
5)
SEM-4 Let G, Ti and Pk be two T- EGG GENBIOM ’s:
(a) A generalized substitution token T-EGG GENBIOM description relation
entity Ti S Tk  .G is interpreted as substituting every Ti in G by Tk.
(b) A multi valued substitution token T-EGG GENBIOM description relation
entity is interpreted as:
Tn S Pn . Tn-1 S Pn-1 ... Tk S Pk  …Pi S T2 .Ti S P1 .G
= Tn S Pn . (Tn-1 S Pn-1 (... (Tk S Pk  …(Pi S T2 .(Ti S P1 G
))…) … )).
2.3 PRAGMATICS FOR GENBIOM ECONOMY GENERATING TASIM
RELATIONAL GENBIOM FORMS
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Definition 3 (a) The following has special meanings in T-EGG TASIM language:
1) “o” is a “memory” or “memory type” dress form.
2) “(” is an “E-GENBIOR type antenna” dress form.
3) “)” is an “E-GENBIOT type antenna” dress form.
4) “(…)” is a “pair of GENBIOM type antenna” dress form.
5) A GENBIOM can be in the state of a dress form type or a body form type.
(b) Let  = {+, -} be a dress forming operator type. Where, + stands for “make
dress form on” and - stands for “make dress form off.” If x is a dress form type and y is a
GENBIOM body type, then in the instructional description relational form type notation:
1) ((+ @ x)@y) means “puts dress form x on GENBIOM body y.”
2) ((-@x)@y) means “takes out dress form x from GENBIOM body y.”
(c) Let  = {+, -} be an injection (or writing) operator type. Where, + stands for
“inject or write into” and - stands for “suck out.” If x and y are two GENBIOM body types
then in the instructional description relational form type notation:
1) ((+@ x)@y) means “inject x into GENBIOM y.”
2) ((-@ x)@y) means “suck x out of GENBIOM y.”
(d) The other operating systems and user operators are defined in the same description
relational form type..
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