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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}. 1 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. 2 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. 3 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) xS(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: 4 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 5 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. 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