WO1982002267A1 - Systeme de manipulation de chaines autonome - Google Patents

Systeme de manipulation de chaines autonome Download PDF

Info

Publication number
WO1982002267A1
WO1982002267A1 PCT/US1980/001729 US8001729W WO8202267A1 WO 1982002267 A1 WO1982002267 A1 WO 1982002267A1 US 8001729 W US8001729 W US 8001729W WO 8202267 A1 WO8202267 A1 WO 8202267A1
Authority
WO
WIPO (PCT)
Prior art keywords
string
signals
cycle
representation
bit
Prior art date
Application number
PCT/US1980/001729
Other languages
English (en)
Inventor
Joel Dov Isaacson
Original Assignee
Joel Dov Isaacson
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Joel Dov Isaacson filed Critical Joel Dov Isaacson
Priority to PCT/US1980/001729 priority Critical patent/WO1982002267A1/fr
Priority to AU71727/81A priority patent/AU7172781A/en
Priority to EP19810901382 priority patent/EP0067810A1/fr
Publication of WO1982002267A1 publication Critical patent/WO1982002267A1/fr

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/76—Arrangements for rearranging, permuting or selecting data according to predetermined rules, independently of the content of the data
    • G06F7/762—Arrangements for rearranging, permuting or selecting data according to predetermined rules, independently of the content of the data having at least two separately controlled rearrangement levels, e.g. multistage interconnection networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/76—Arrangements for rearranging, permuting or selecting data according to predetermined rules, independently of the content of the data

Definitions

  • the present invention is in the field cf data processing, and in the subfield of artificial or machine intelligence. It has become customary in the art to view computing machines broadly as symbol-manipulation devices. Normally, symbols arranged in some initial structural configuration (often strings, or data-structures reducible to strings) are input to a computing system and manipulated according to some well-defined and well-sequenced instructions (program) into some other, sought-after, configuration of symbols, constituting the output or result. Given an input configuration, the preparation of a program to achieve a desired end-result is usually a premeditated task, involving an objective or goal, intention, design, and other volitional and intelligent activities of a human programmer.
  • the present invention is likewise concerned with symbol-manipulation and, in particular, with the manipulation of representations of finite strings of arbitrary symbols.
  • the basic system has no programming capabilities (at least in the sense described above), and, regardless of the type of input, the same type of manipulation is applied in a blind, purposeless, and primitive fashion.
  • the system has no prior knowledge of its environment, and its basic capability is discriminating between adjacent symbols as being distinct or indistinct, and recording the results of such discrimination in an internal code of four letters.
  • the system is not concerned with external symbols qua symbols, and therefore no internal description or explicit recognition of these is necessary.
  • autonomic processing The ability of an automatic symbol-manipulation system to produce unexpected global results (which are not trivial, and are “meaningful” or “useful"), strictly on the basis of local, myopic, primitive, and purposeless manipulation of symbols, is referred to in this invention as "autonomic processing.” It turns out that the system, operating in an autonomic mode of processing, transforms any input string into a DNA-like structure and retains this structure indefinitely in a self-created mode of memory. The processing activity itself, when looked at carefully and analyzed in the large, displays features of classical dialectical activity, in effect mimicking Hegelian dialectic with uncanny fidelity.
  • String-manipulation operations on whole strings are the basic ingredients of the system disclosed hereinafter.
  • the level and function of these operations are comparable to those of machine operations and instruction sets in conventional data processing systems.
  • the operations disclosed are classified as primary, including Interface Tetracoding (ITC), Tetracoding (TTC), Triunation (TRI), Lagging (LAG), and Wagging (WAG); and auxiliary, including Streaking (STR), Reclamation (REC), Bicoloring (BIC), Amination (AMN), Deamination (DMN), and four types of Ideographing (IDA, IUB, IDC, and IDD).
  • the primary operations are closely related and are functionally equivalent, when augmented by the proper auxiliary operations.
  • String-manipulation systems defined by them are subsumed under Post's monogenic normal systems which are known to be very powerful computationally.
  • the auxiliary operations essentially perform certain trans lations between primary modes, and ideographing operations generate ideographic representations of internal strings for output and display purposes.
  • the primary operations, aided by the auxiliary, form a basis for a powerful string-manipulation system, expressible in a sort of higherlevel calculus of operations, that can be used effectively to define and carry out certain processes of industrial utility.
  • BIP Basic Intellector Process
  • BIP processing include: autonomic mode of processing; generation of tetracodes belonging to a substrate tree; operative dialectic and manifested (structural) dialectic; autonomic mode of memory; and autonomic error-correction.
  • BIP has numerous variations that are essentially functionally equivalent to it. Such variations are generically called “hegelizing processes," and BIP s , which amounts to repetitive triunation of the streak of a given string and its successors, is such a process.
  • a preferred hardware embodiment, in terms of logic design diagram for electronic circuitry, of TRI and BIP s is completely specified and is referred to as INTELLECTOR.
  • a single INTELLECTOR, or a plurality of INTELLECTORs can be connected to other digital systems, including digital data processing means, and, in particular, to a control section of a digital computer having memory and control sections; such combinations having the advantages of both the autonomic string-manipulation system inherent in INTELLECTORs, and the programinability of conventional digital computer systems.
  • Figure 1 illustrates diagramatically relationships among the operations TTC, TRI, STR, REC, ITC, and BIC.
  • Figure 2 illustrates schematically the processes BIP and BIP and the relationship between them.
  • Figure 3 illustrates a tree of rank n.
  • Figure 4 comprises Figures 4A, 4B, 4C, 4D, and 4E and shows a trace of an example of BIP processing written in the internal alphabet (Figure 4A); and in ideographic representations type IDA ( Figure 43), type IDB (Figure 4C), type LDC ( Figure 4D), and type IDD ( Figure 4E).
  • Figure 5 shows a trace of an example of BIP processing written in the internal alphabet.
  • Figure 6 is a schematic representation of BIP processing.
  • a "string,” consisting of individual “elements,” is a linear arrangement of said elements.
  • the “length” of a string is the number of elements in the linear arrangement.
  • a string of length n is said to be “n units long.”
  • a “substring” of a string of length n is any portion thereof of length m, for 1 ⁇ m ⁇ n. All strings herein are of finite length, or simply “finite,” and normally (but not necessarily) are at least three units long. Given a string, an element at one of its ends is referred to as “leftmost" or "first” element.
  • the element next to the first is said to be on its "right” and called “second” element, and so on, until the rightmost element, referred to as “last” element.
  • the first element is deemed to have a special empty or “blank” element on its left, and the last element is deemed to have a blank element on its right. Blank elements do not contribute units to the length of a string, and, normally, no blank elements appear between the first and the last elements.
  • a string, together with its blank elements, is referred to as "closed,” and without them as “open.”
  • a string is deemed to be closed unless specifically referred to as open.
  • Each element in the open portion of a closed string has a "leftneighbor,” i.e., the element immediately to its left, and, likewise, a right-neighbor; the first and last elements having a blank left-neighbor and a blank right-neighbor, respectively.
  • An element that can be prehended or sensed or recorded by human beings, and/or other living things or systems, and/or instruments, devices, or systems made by human beings, is referred to as an objective element or "datum-object.”
  • An element that cannot be prehended, sensed, or recorded by any of said means is referred to as "fantomark.”
  • a string comprising elements which are not datum-objects is referred to as “fantomark string.”
  • Marks and symbols are considered to be datumobjects, and, normally, strings herein are strings of marks or symbols, or their physical representations, such as in terms of bit-signal patterms.
  • a mark is normally considered only in the context of a string, namely in the context of other marks, including blanks; consequently, marks are reduced to essentially syncategorematic entities, or even weaker.
  • marks are taken individually or even in combination, any meanings, significations, or other semiotic properties are normally disregarded.
  • a mark is normally considered in terms of its relations to its two neighbors, a “relation” taken to be binary distinction/indistinction; namely, a mark is said to be "distinct” from a neighbor if it is distinguishable from the neighbor (by some comparison means); otherwise it is said to be “indistinct” from the neighbor.
  • a relation between two marks is symmetric, or mutual.
  • the essential information in a mark string is the totality of mutual relations of elements in the string.
  • This information can be encoded in a number of ways which are essentially equivalent, or commutable into each other, and thus reducible to a single encoding method.
  • the two techniques below, describing "streaking" and “tetracoding,” disclose the essence of said encoding.
  • the "streak" of a string is a binary string, i.e., a string having at most two types of marks such as '0' and '1', that encodes the mutual relations of elements in the former string in the following manner: for each element, but the first, in the open portion of said string, if it is distinct from its left-neighbor the corresponding code in the streak is 0; otherwise it is 1.
  • a 0 is appended to each end of the code sequence. A streak without the appended 0's is referred to as "bare" streak.
  • the "tetracode" of a string is a mark string that encodes the mutu ⁇ al relations of elements in the original string in the following manner: for each element in the open portion of the original string, if both neighbors are distinct from it the corresponding code is a mark 'A'; if the left-neighbor is distinct and the right-neighbor is indistinct from it the corresponding code is a mark 'B'; if the left-neighbor is indistinct and the right-neighbor is distinct from it the corresponding code is a mark 'C'; and if both neighbors are indistinct from it the corresponding code is a mark 'D'.
  • the set of marks consisting of A, B, C, and D is referred to as "internal alphabet," and the. marks are sometimes referred to as "letters.” Ideographic symbols may be substituted for the letters, for example: ⁇ for A; ⁇ for B; ⁇ for C; and for D.
  • a method of generating streaks of mark strings is referred to as “streaking method” and the transformational operation involved is referred to as “streaking”; likewise, a method of generating tetracodes is referred to as “tetracoding method” and the operation as “tetracoding.”
  • streaking method A method of generating streaks of mark strings
  • tetracoding method a method of generating tetracodes
  • tetracoding method a method of generating tetracoding method
  • tetracoding method the transformational operation involved
  • Fantomark strings which, by definition, are imperceptible to man, animal, or machine may nevertheless have well-defined streaks, which are ordinary mark strings.
  • This invention is not concerned with methods of generating streaks of fantomark strings; however, it includes methods of processing streaks of fantomark strings, if such are presented for processing, in the same manner as any other streaks.
  • the present invention is concerned with operations on strings, with processes defined in terms of said ⁇ perations, with devices that embody said processes, and with combinations, or interactions, of said processes and devices with conventional data processing systems to effect certain useful processing of data.
  • String-manipulation operations on whole strings are the basic ingredients of the system herein disclosed. The level and function of these operations are comparable to those of machine operations and instruction sets in conventional data processing systems. All string-manipulation operations are "unary,” i.e., operate on a single string, the "operand.” Normally an operation includes a set of rewriting rules (or productions) out of which a rule is selected and applied to each mark in the operand in the course of application of the operation. Most rewriting rules are context-sensitive, namely intrinsically selected for application to a given mark on the basis of its local context.
  • Context-sensitive rewriting rules are written in the format: X ⁇ U/Y-Z, meaning that "the mark X is to be rewritten as the mark U if X is in the context of the mark Y and the mark Z, on its left and right, respectively.”
  • Other standard, or self-explanatory, formats for rewriting rules and productions are used, as needed.
  • An operation involving simultaneous applications of rewriting rules to all marks in the operand is referred to as "parallel”; and the simultaneous acts are collectively referred to as transformational step, or "step.”
  • any use of the word 'step' in the claims included in this application is not governed by this definition.
  • a sequential transformational step comprises, temporally and functionally, the sequence of individual substaps involved in the application of the sequential operation.
  • An operation that is not parallel and not strictly sequential is referred to as "scrambled.” Most operations herein disclosed are parallel and some are sequential. It is obvious to persons skilled in the art that all parallel operations can be converted into sequential, or even scrambled, operations without altering their essential character.
  • a string resulting from application of a string-manipulation operation to an operand is referred to as "result” or (immediate) “successor,” and the operand is referred to as (immediate) “predecessor” of the successor.
  • input string is synonymous with operand or predecessor; and “output string” is synonymous with result or successor.
  • a string-manipulation operation is referred to as "monogenic, " if its application to an operand yields at most one successor. Note, the number of predecessors yielding the same successor under same monogenic operation is not restricted to one. All operations herein disclosed are monogenic.
  • strings are designated by the following types and notations.
  • the tetracode and streak of a string Q are written T(Q) and S(Q), respectively. Subscripts are used to distinguish between two or more strings of the same type.
  • OPR i Application of OPR i to the successor of Q under OPR j is written OPR i (OPR j (Q)), and this notation is extended to any number of applications of various operations, as needed.
  • the notations ' ⁇ ' and ' ' designate the phrases "distinct from” and “indistinct from,” respectively.
  • the specifications of string-manipulation operations are disclosed and set forth below.
  • TTC (AAAABCAAA) BDDCAABDC; length: 9
  • the bare streak is: 11100011 ; length: 8 Operation Name: Triunation
  • b i-1 is the color-value assigned to t i-1 , i.e.,
  • ⁇ b i-1 is the color-value opposite to the one assigned to t i-1 .
  • the three leftmost symbols uniquely determine a rewriting rule from the set below that specifies a symbol ⁇ ⁇ 0,1, ⁇ to be appended to the R.H.S. of the string; the leftmost symbol is dropped and same is repeated until s n-1 is dropped, which completes one transformational operation on the entire string.
  • the general format of the rewriting rules is:
  • L 1 000 ⁇ 1 L 9 : ⁇ 00 ⁇ 1 L 13 : 0 ⁇ 0 ⁇ ⁇ L 17 : 00 ⁇ ⁇ 1 L 2 : 001 ⁇ 0 L 10 : ⁇ 01 ⁇ 0 L 14 : 0 ⁇ 1 ⁇ ⁇ L 18 : 01 ⁇ ⁇ 0L 3 : 010 ⁇ 0 L 11 : ⁇ 10 ⁇ 0 L 15 : 1 ⁇ 0 ⁇ ⁇ L 19 : 10 ⁇ ⁇ 0L 4 : 011 ⁇ 0 L 12 : ⁇ 11 ⁇ 0 L 16 : 1 ⁇ 1 ⁇ ⁇ L 20 : 11 ⁇ ⁇ 0 L 5 : 100 ⁇ 0 L 6 : 101 ⁇ 0 L 7 : 110 ⁇ 0
  • L 9 , L 2 , L 3' L 5 , L 1 , L 1 , L 1 , L 17 , and L 14 to ⁇ 00, 001, 010, 100, 000,
  • the three leftmost symbols uniquely determine a rewriting rule from the set below that specifies a symbol ⁇ ⁇ N 1 ,N 2 , ...,N 20 ⁇ which becomes a symbol in the new stringy the leftmost symbol is dropped and same is repeated until s n-2 is dropped.
  • the new string thus comprises n-1 N i 's in the order of their production.
  • the general format of the rewriting rules is:
  • Type - unary, sequential
  • v 1 Starting at v 1 , v 1 together with the last v in the string, determine a unique rewriting rule from the set below that specifies a symbol ⁇ ⁇ N 1 , ..., N 20 ⁇ to be appended to the R.H.S. of the string; v 1 is dropped and same is repeated until v n-1 is dropped and then the first appended symbol is dropped, which completes one transformational operation on the string.
  • the general format of the rewriting rules is: v i $v last ⁇ N j , l ⁇ j ⁇ 20, depending on v i and v last , where $ is any substring; for 1 ⁇ i ⁇ n-1.
  • the explicit rewriting rules are:
  • W 1 N 1 $N 1 ⁇ N 2 W 9 : N 1 $N 9 ⁇ N 2 W 13 : N 1 $N 13 ⁇ N 10 W 17 : N 1 $N 13 ⁇ N 14 W 2 : N 1 $N 2 ⁇ N 4 W 10 : N 1 $N 10 ⁇ N 4 W 14 : N 1 $N 14 ⁇ N 12 W 18 : N 1 $N 18 ⁇ N 16 W 3 : N 1 $N 3 ⁇ N 6 W 11 : N 1 $N 11 ⁇ N 6 W 15 : N 1 $N 15 ⁇ N 10 W 19 : N 1 $N 19 ⁇ N 14 W 4 : N 1 $N 4 ⁇ N 8 W 12 : N 1 $N 12 ⁇ N 8 W 16 : N 1 $N 16 ⁇ N 12 W 20 : N 1 $N 20 ⁇ N 16 W 5 : N 1 $N 5 ⁇ N 2 NOTE: If, in rewriting rules W 1 through W 20 , the first
  • W 7 N 1 $N ⁇ N 6 symbols N 8 , N 9 , or N 17 , the same rules apply to these symbols, respectively.
  • W 8 N 1 $N 8 ⁇ N 8 W 21 : N 2 $N 1 ⁇ N 1 W 29 : N 2 $N 9 ⁇ N 1 W 33 : N 2 $N 13 ⁇ N 9 W 37 : N 2 $N 17 ⁇ N 13 W 22 : N 2 $N 2 ⁇ N 3 W 30 : N 2 $N 10 ⁇ N 3 W 34 : N 2 $N 14 ⁇ N 11 W 38 : N 2 $N 18 ⁇ N 15 W 23 : N 2 $N 3 ⁇ N 5 W 31 : N 2 $N 11 ⁇ N 5 W 35 : N 2 $N 15 ⁇ N 9 W 39 : N 2 $N 19 ⁇ N 13 W 24 : N 2 $N 4 ⁇ N 7 W 32 : N 2 $N 12 ⁇ N 7 W 36 : N 2 $N 16 ⁇ N 11 W 40 : N 2 $N 20 ⁇
  • DMN Type - unary, parallel Input String: Type: AMN (S) (bare)
  • N 13 through N 16 can ⁇
  • N 3 ⁇ 1 (11) N 11 ⁇ 1 not appear is an aminated
  • DMN(N 11 N 5 N 1 N 2 N 4 N 8 N 8 N 20 ) ⁇ 10001111 ⁇ ; length: 10; bare length: 8
  • n Format See FIGS . 4B, 4C, 4D, and 4E
  • ITC is a generic form of TTC; the former tetracodes arbitrary raw-data strings and the latter is a specialized version that tetracodes only strings written in a fixed 4-letter alphabet.
  • TTC is considered the most important primary operation and the remaining operations will be discussed in reference to it.
  • ITC and STR are normally interface operations and may be subsumed under certain pre-processing operations briefly described below.
  • preprocessing means The collection of all means available for pre-processing is referred to as "preprocessing means.” This invention is not concerned with various technologies of pre-processing means and it is presupposed that, included in any given type of pre-processing means, there is a suitable comparison means, or equivalents thereof, for determining distinction/indistinction of elements; so that, given such comparison means, implementation of ITC or STR is straightforward.
  • analog-to-digital conversion means may be included, and the comparison means may be digital. If elements in Q cannot be sensed and recorded directly, means for detecting and recording distinctions between elements, rather than the elements themselves, may be used, which recording providing the essential information for S(Q). Lastly, if streaks of fantomark strings are detected and recorded by some means, the streaks thus recorded can be further processed by the system as any other streaks. Interrelationships among TTC, TRI, STR, REC, ITC, and BIC are illustrated diagramatically in FIG. 1. From said diagram,
  • T i+1 can be obtained from T i-1 or T i in a number of ways, including the following,
  • TTC can be served by TRI, LAG, or WAG, when augmented by the proper auxiliary operations, as specified above.
  • TTC through TRI, LAG, and WAG may seem superfluous but are, in fact, essential to the definition of scope of this invention.
  • TRI will be brought out later in connection with a certain device embodiment of this invention.
  • the basic roles of LAG and WAG are discussed below.
  • auxiliary operations essentially perform certain translations between the primary modes.
  • Certain basic uses of STR, REC,AMN, DMN, and BIC are demonstrated earlier.
  • IDA, IDB, IDC, and IDD generate ideographic representations of tetracodes for output and display purposes.
  • IDD is used also in connection with the process of abduction discussed elsewhere.
  • the primary operations, aided by the auxiliary form a basis for a powerful string-manipulation system, expressible in a sort of higherlevel calculus of operations, that can be used effectively to define and carry out certain processes of industrial utility. Processes & Processing
  • BIP is introduced as a natural extension of said processes, followed by detailed analysis and discussion of the properties and behaviour of BIP processing, including the following topics: autonomic mode of BIP processing; the tetracode space; operative dialectic and the Hegelian connection; manifested dialectic; two concrete examples of BIP processing; autonomic error-correction; and functional equivalents of BIP.
  • a process of degree 1 is said to be “elementary.”
  • a process of degree m, where m is finite, is said to be “finite,” and if m is unbounded or indefinite the process is said to be “indefinite.” Indefinite degree is denoted by ⁇ .
  • a process is said to be “monogenic” if all operations involved in it are monogenic. All processes herein disclosed are monogenic. Hereinafter processes normally involve tetracodes, or, in the alternative, their streaks.
  • a substring of a tetracode consisting of two or more A's is referred to as "quid.”
  • a quid is said to be disconnected or "discrete.”
  • a substring of a tetracode consisting of a B followed by a C, or a B followed by one or more D's followed by a C is referred to as "quod.”
  • a quod is said to be integrated or "connected.”
  • a substring of a tetracode consisting of a single A is referred to as "monad,” and may be considered as either a unitary quid or a unitary quod, depending on its history in a transformational process.
  • a quid or quod of odd or even length is referred to as "odd” or “even” quid or quod, respectively.
  • odd odd or even length
  • odd even quid or quod
  • a quid or quod of length k is written QUID k or QUOD k , respectively, or without subscript if length is understood or irrelevant.
  • the "liquidation sequence" of a quod of length m is a sequence of strings, each of length m, such that the i th string, for 1 ⁇ i ⁇ , con ⁇ sists of a quod of length l»m-2i, for m-2 ⁇ l ⁇ 0,preceded by a substring of length i having an A in the rightmost position, and followed by a substring of length i beginning with A.
  • a process for generating the liquidation sequence of a quod is referred to as "liquidating process,” the processing involved is referred to as “liquidating,” and thequod is said to be liquidated.
  • the string before last has 'BC' or 'BDC', respectively, for its residual quod, and the final liquidating step yields 'AA' or 'AAA' , respectively, in the middle of the last string in the liquidating sequence.
  • the following scheme illustrates the structure of the liquidating sequence of an even quod.
  • Liquidator is a liquidating process and, in fact, liquidates a quod of length m ⁇ 2 in exactly steps. It is observed that, during liquidation, a quod is "peeled off” '"or “skinned” at each end, one unit length at a liquidating step, and the two severed units appear as monads in the next string. This process continues until the entire quod has been dissolved into monads. Now, going in the other direction, viewing a quid as a collection of monads (perhaps chipped earlier from some quods), it is shown below how a quid can be integrated back into a quod.
  • Quodizing process A process transforming a quid into a quod of same length is referred to as “quodizing process,” the processing involved is referred to as “quodizing,” and the quid is said to be quodized.
  • Quodizer Mnemonic QDZ Type: finite; elementary
  • said patterns are obviously not programmed in any conventional sense, as one identifies them only after the fact, rather than specifies them in a program, scheme, or procedure beforehand; or, put another way, there is no obvious way, known at present in the art, to relate an ultra broad procedure such as TTC ⁇ (T 1 ) to the highly specific type of outcome engendered by it, or view it as "premeditated programming" of such outcome.
  • a string in the internal alphabet is referred to as "well-formed” (w.f.) if it consists of one or more quids and/or one or more quods arranged in any way; as “strictly well-formed” (s.w.f.) if it consists of a single quid or a single quod, or an arrangement of one or more quids and one or more quods in alternation; and as “weakly well-formed” (w.w.f.) if it is w.f. but not s.w.f. Any tetracode is w.f. and any w.f. string is a tetracode.
  • a tetracode generated from a string which is not a tetracode may be w.w.f. or s.w.f.; a tetracode generated from a tetracode is s.w.f.
  • n there exist 4 distinct strings in the internal alphabet; exactly 2 n-1 of these are w.f., the s.w.f. form a proper subset of the w.f., and the rest are w.w.f.
  • the number of s.w.f; strings, SWF(n), for n>2 can be determined from the following formula.
  • a tree of rank n is of height n and is described as follows (see FIG. 3). The root and each node, to level n-3 on the L.H.S. and to level n-2 on the R.H.S., has exactly two successors.
  • A The root is labeled A, and, recursively, successors of A are labeled (left & right): A & B; successors of B: C & D; successors of C: A & B; and successors of D: C & D.
  • a & B successors of B
  • C successors of C
  • a & B successors of D
  • D C & D.
  • level n-3 on the L.H.S. at level n-2 each node has only a left successor, and at level n-l all nodes are terminal, i.e., without successors.
  • At level n-2 on the R.H.S. at level n-1 each node has only a left successor, and at level n all nodes are terminal.
  • an edge connecting two A's or two D's is labeled 1, and all other edges are labeled 0.
  • a tetracode must begin with either A or B. If it begins with A, it can be identified with a unique path in the tree by entering at the root and proceeding to successive nodes by following the remaining letters in the tetracode. The path terminates at a terminal node on the L.H.S., or an A or a C node at level n-1 on the R.H.S. Similarly, a tetracode beginning with B can be traced by entering at the B node at level 2; the path terminates at a terminal node on the R.H.S. Note that as a tetracode is traced through the nodes, its bare streak is traced through the edges connecting said nodes.
  • a tree is said to be "absorbed” by another tree if all its nodes and respective edges, together with their labels, appear in (part of) the latter, "absorbing" tree.
  • Any tetracode of length n is said to be traceable, or "absorbed" by a tree of rank n in a unique way; and said tree absorbs exactly the collection of tetracodes of length n. Since all tetracodes are finite, the corresponding absorbing trees are of finite rank. However, in this connection, it is useful to define a binary tree of unbounded rank, by using the previous recursive definition for trees of finite rank without the restriction on the level up to which the recursion applies.
  • a rooted binary tree is obtained, where the root is labeled A and the tree extends indefinitely; it is referred to as "substrate tree.”
  • substrate tree any tree of finite rank is absorbed By a substrate tree in an infinite number' of ways, or in a finite number of ways if some large enough portion of' the substrate tree is considered.
  • every tetracode is uniquely absorbed by a finite tree and every finite tree is absorbed by a substarte tree, the entire collection of string productions of BIP, and certain string-manipulation systems derived from it, is absorbed, or embedded, in a substrate tree.
  • all strings generated and manipulated within said systemsj in tetracode or streak modes are realized as sequences of nodes or edges, respectively, on paths in a substrate tree.
  • the tetracode space is realized in a substrate tree.
  • Another important element of these discovery and invention is an apparent dialectical dynamics that shapes the tetracodes generated by BIP processing;, said dynamics is brought out and exemplified below. From the definitions of the processes LQD, QDZ, and BIP, it is clear that, in each step of BIP processing each quod undergoes a liquidating step and each quid is quodized, and nothing else occurs. Consequently, BIP processing amounts to endless disintegration of quods into quids and recombination of quids into quods, mitigated by a kind of internal, autonomic, delicate balancing mechanism.
  • quids are "discrete” whereas quods are "connected.” So, to repeat, whatever these entities may be and whatever they may signify, contrariety is their essence. While discreteness and connectedness are obvious contraries or opposites, particularly important in structural matters, (note here a pertinent quote from Hermann Weyl ("Symmetry," p. 109): “The splitting into something discrete and something continuous seems to me a basic issue in all morphology."), other contrary pairs may be assigned to quids and quods as interpretants, and BIP processing analyzed in terms of such assignments.
  • BECOMING continually mediates the dissolution of BEING into NOUGHT and the passage of NOUGHT into BEING.
  • a s.w.f. tetracode is referred to as "thesis,” if none of its quods is of length greater than 3.
  • the successor of a thesis under TTC is referred to as "antithesis.”
  • a thesis and its antithesis are related in such a way that under each quid and each quod in the thesis there is a quod or quid, respectively, of same length in the antithesis.
  • An antithesis is said to be “complementary" to its thesis, and together are said to constitute a .
  • Respective complementary substrings are referred to as a pair of “dialectical substrings.”
  • the successor of an antithesis under TTC is referred to as "synthesis.” Under each quid in an antithesis there is a quod of same length in the synthesis; under each quod of length m>3, there are a monad followed by a quod of length m-2 followed by a monad.
  • a synthesis is said to have a structure that "mediates" the structures in the complementary pair preceding it, in the sense that each pair of dialectical substrings of length > 3 yields a partly discrete and partly connected (symmetrical) substring in the synthesis; and, if said length is ⁇ 3 and no such symmetrical resolution is possible, the synthetic substring normally takes on the character, i.e., quid or quod, of the respective substring in the thesis.
  • the above intricate rules of complementarity and mediation are derived from observation after the fact, as opposed to being programmed into BIP in advance.
  • a thesis, its antithesis, and the following synthesis are referred to as (perfect) "dialectical triad « The following description is supported by.
  • the first string generated, T 1 is referred to as the "surface-structure" of the external or initial string, R.
  • T 1 may be w.w.f. or s.w.f., depending on the inherent structure of the initial string R. All successive tetracodes are s.w.f.
  • a cycle referred to as "Hegelian cycle” (H.C.)
  • H.C. Hegelian cycle
  • Tetracodes in the range between the surface-structure and the beginning of a cycle are referred to as "intar mediate.”
  • Tetracodes in a H.C. are referred to as "deep” or “internal.”
  • the first tetracode in a H.C. is a thesis, referred to as "deep structure” or IDEA of R. A deep structure together with its antithesis are referred to as "canonical form" of R.
  • a canonical form can be adequately characterized as 'information structure comprising a complementary pair of 4-letter strings', which characterization bearing a striking resemlance to that of a DNA molecule, although the complementarity rules appear to be somewhat different; hence, the structure of a canonical form is said to be "DNA-like."
  • the first triad which includes a canonical form, is normally a perfect dialectical triad. Successive triads are frequently also perfect dialectical triads, but may have certain perturbations or imperfections, especially if the lengths of tetracodes and the cycle itself are large.
  • the number of intermediate tetracodes may be zero or larger, and they may or may not be organized in dialectical triads; often some do and some do not.
  • Memory or more specifically 'dynamic memory' is inherent in this process.
  • the surface-structure is said to be in transitory “subsurface memory”; intermediate strings in transitory “intermediate memory”; and strings of the Hegelian, cycle are said to be in "deep memory.”
  • deep memory is a type of dynamic memory that retains its information indefinitely.
  • the trace displays the following basic features. Tet(01) is the surface-structure of 'BEGINNING', and is followed by eight intermediate tetracodes, Tet (02) through Tet(09) , all of which appear only once in this processing. Tet(lO) is the first tetracode which is repeated in the sequence i.e., with the appearance of Ter(22), so that the Hegelian cycle consists of the twelve strings Tet(10) through Tet(21). These are organized in exactly four triads, each of which happens to be a perfect dialectical triad. The triads are:
  • Triad 1 Tet(10) ⁇ Tet(11) ⁇ Tet(12)
  • Triad 2 Tet(13) ⁇ Tet(14) ⁇ Tet(15)
  • Triad 3 Tet(16) ⁇ Tet(17) ⁇ Tet(18)
  • Triad 4 Tet(19) ⁇ Tet(20) ⁇ Tet(21), where columns T, A, and S list theses, antitheses, and syntheses, respectively. Analyze in some detail one of the triads, say triad 2, using ideographic representation type IDB (see FIG. 4C) : d - discrete (quid) c - connected (quod) m m - mediated m'- mediated for short substrings
  • BIP does not have access to stored programs or external references; is not supplied with any definitions of "strings,” “substrings,” “discreteness,” “connectedness,” “complementarity,”, “mediation,” or the like; and is not given any rules of inference or any other rules beyond the extremely primitive rewriting rules of TTC.
  • the rewriting rules of TTC are strictly local, acting in parallel, and myopic, i.e., cannot "see” beyond the string on which they operate, and, within it, each rewriting rule sees at most three contiguous symbols; also, there is no transfer of information across a string to obtain a global view of it.
  • the transformational activity is strictly local and spontaneous, yet it produces global results. It resembles a chemical reaction taking place local ly on an exposed photographic plate, that, combined with numerous others, yield a global picture. It is anticipated that, in addition to electronics, implementation in chemical or biochemical systems is particularly suitable for this kind of a process.
  • Tet(Ol) is the surface-structure, and also the first string in the Hegelian cycle, repeated as Tet(31); (no intermediate tetracodes occur in this example).
  • the cycle consists of thirty strings, Tet(Ol) through Tet(30), organized in ten triads, some of which are perfect (P) , some are modified (M) , and some are imperfect (I), dialectical triads.
  • P perfect
  • M modified
  • I imperfect
  • Triad 1 Tet(04) ⁇ Tet(02) ⁇ Tet(03)
  • Triad 4 Tet(10) ⁇ Tet(11) ⁇ Tet(12) I Triad 5: Tet(13) ⁇ Tet(14) ⁇ Tet(15) P
  • Triad 8 Tet(22) ⁇ Tet(23) ⁇ Tet(24) M
  • Type 1 next-step correction
  • Type 2 regenerated-cycle correction
  • Type 3 correctness without correction
  • Tet(09) Arbitrarily, take Tet(09) from trace in FIG. 5.
  • Tet(09) Because of noise or malfunction, errors have been introduced in Tet(09) to the point where it does not even bear a resemblance to its original make-up or structure, and is not even well-formed; for example,
  • FIG. 4A may end up looking like the following:
  • BIP The relationship between BIP and BIP is illustrated schematically in FIG. 2.
  • BIP s is said to "shadow" BIP, and since any T i can be recovered from the corresponding S i by application of REC to S i , BIP and BIP are essentially functionally equivalent.
  • BIP s appears to be simpler to implement in digital technology, and a preferred embodiment of BIP is given in the next section.
  • hegelizing process is used for such processes. Included among said processes are BIP-simulators, i.e., processes designed or programmed to produce effects of BIP processing, but not necessarily through autonomic modes of operation. A string processed by a hegelizing process is said to undergo “hegelization,” and the processing involved is referred to as "hegelizing.” BIP s is an example of a hegelizing process.
  • Such implementation may include, but is not limiced to, the use of software and/or hardware digital technologies; including, but not limited to, hard-wired logic circuitry; micro-instructions or microcode stored in read-only memory, or in writable control store, or in other types of memories; and programming of said operations or processes in higher-level computer languages, such as FORTRAN or PL/1 or PASCAL, in conjunction with the use of general-purpose electronic digital computers to carr out said operations or processes.
  • software and/or hardware digital technologies including, but not limited to, hard-wired logic circuitry; micro-instructions or microcode stored in read-only memory, or in writable control store, or in other types of memories; and programming of said operations or processes in higher-level computer languages, such as FORTRAN or PL/1 or PASCAL, in conjunction with the use of general-purpose electronic digital computers to carr out said operations or processes.
  • implementation may include, but i not limited to, the use of chemical or biochemical methods and means; including, but not limited to, the use of artificial or natural materials and substances such as nucleotides, nucleic acids such as DNA, RNA and their many varieties, amino acids, proteins, and the like; said substances being in living or non-living states, within or without living cells; provided that natural mental processes carried out in unaided living human brains are not construed as implementations.
  • a bare streak of length n-1, represented by bit-signals, is fed via input lines 1 to n-1 binary cells 2 of an (n-1)-bit register, such that the i th cell receives the bit-signal s i , for 1 ⁇ i ⁇ n-1.
  • s i for 2 ⁇ i ⁇ n-2, is compared simultaneously with s i-1 and s i+1 in the following manner: s i and s i-1 are input, via respective connecting lines, to AND gate 3, and, simultaneously, to NAND gate with negated inputs 4; the outputs from 3 and 4 are input, via respective connecting lines, to OR gate 5; similarly, s.
  • s 1 and s 2 are input, via respective connecting lines, to NAND gate with negated inputs 4, and the output from 4 is made available, with proper delay, to output line 9, whereupon one TRI ste is completed.
  • feedback line 8 is included, and output from 4 is fed back, with proper delay, to cell 2, designated s 1 , whereupon the nex TRI step starts.
  • s n-1 , and s n-2 are input, via respective connecting lines, to NAND gate with negated inputs 4, and the output from 4 is made available, with proper delay, to output line 9, where upon one TRI step is completed.
  • LECTOR. or a plurality of INTELLECTORs, can be readily connected, via input lines 1 and output, lines 7 & 9 (see FIGS. 7, 7A, and 7B) to other digital systems, including digital data processing means; and, in particular, to a control section of a digital computer system having memory and control sections; such combinations having the advantages of both the autonomic string-manipulation system inherent in INTELLECTORs, and the programmability of conventional digital computer systems. Further, said combinations can be connected to analog systems via analog-to-digital and/or digital-toanalog means.
  • the scope of the present invention includes any and all such combinations, and any and all data processing methods and procedures made possible by virtue of said combinations.

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Machine Translation (AREA)

Abstract

Procedes et moyens dans le domaine du traitement de donnees, concernant l'intelligence artificielle. Ceci concerne des chaines finies de symboles arbitraires, et leur manipulation, y compris des operations sur les chaines, des procedes definis en terme de ces operations, des dispositifs qui mettent en oeuvre ces procedes, et des combinaisons de ces procedes et dispositifs avec des systemes conventionnels de traitement de donnees pour effectuer un traitement utile des donnees. L'operation et le procede les plus importants sont, respectivement, le Tetracodage (TTC), et 'Basic Intellector Process'(BIP) (FIG. 6). 'INTELLECTOR' est une realisation du 'hardware' de 'BIP's, qui est une variante fonctionnellement de'BIP'. Un ou plusieurs 'INTELLECTORs' (FIG. 7, 7A et 7B) peuvent etre connectes a des systemes conventionnels de traitement de donnees numeriques, combinant leur capacites respectives autonomes et programmees de traitement de donnees.
PCT/US1980/001729 1980-12-24 1980-12-24 Systeme de manipulation de chaines autonome WO1982002267A1 (fr)

Priority Applications (3)

Application Number Priority Date Filing Date Title
PCT/US1980/001729 WO1982002267A1 (fr) 1980-12-24 1980-12-24 Systeme de manipulation de chaines autonome
AU71727/81A AU7172781A (en) 1980-12-24 1980-12-24 Autonomic string-manipulation system
EP19810901382 EP0067810A1 (fr) 1980-12-24 1980-12-24 Systeme de manipulation de chaines autonome

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
PCT/US1980/001729 WO1982002267A1 (fr) 1980-12-24 1980-12-24 Systeme de manipulation de chaines autonome
WOUS80/01729801224 1980-12-24

Publications (1)

Publication Number Publication Date
WO1982002267A1 true WO1982002267A1 (fr) 1982-07-08

Family

ID=22154704

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/US1980/001729 WO1982002267A1 (fr) 1980-12-24 1980-12-24 Systeme de manipulation de chaines autonome

Country Status (3)

Country Link
EP (1) EP0067810A1 (fr)
AU (1) AU7172781A (fr)
WO (1) WO1982002267A1 (fr)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4914623A (en) * 1986-09-18 1990-04-03 Hudson-Allen Limited Digital processing of sensor signals for reading binary storage media

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3106699A (en) * 1958-10-07 1963-10-08 Bell Telephone Labor Inc Spatially oriented data processing apparatus
US3196398A (en) * 1962-05-21 1965-07-20 Ibm Pattern recognition preprocessing techniques
US3899771A (en) * 1971-08-17 1975-08-12 Philips Corp Method of character recognition by linear traverse employing shifted edge lines
US4003022A (en) * 1974-08-02 1977-01-11 Nippon Electric Company, Ltd. Symbol string pattern recognition equipment
US4060713A (en) * 1971-06-23 1977-11-29 The Perkin-Elmer Corporation Analysis of images
US4167728A (en) * 1976-11-15 1979-09-11 Environmental Research Institute Of Michigan Automatic image processor

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3106699A (en) * 1958-10-07 1963-10-08 Bell Telephone Labor Inc Spatially oriented data processing apparatus
US3196398A (en) * 1962-05-21 1965-07-20 Ibm Pattern recognition preprocessing techniques
US4060713A (en) * 1971-06-23 1977-11-29 The Perkin-Elmer Corporation Analysis of images
US3899771A (en) * 1971-08-17 1975-08-12 Philips Corp Method of character recognition by linear traverse employing shifted edge lines
US4003022A (en) * 1974-08-02 1977-01-11 Nippon Electric Company, Ltd. Symbol string pattern recognition equipment
US4167728A (en) * 1976-11-15 1979-09-11 Environmental Research Institute Of Michigan Automatic image processor

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4914623A (en) * 1986-09-18 1990-04-03 Hudson-Allen Limited Digital processing of sensor signals for reading binary storage media

Also Published As

Publication number Publication date
EP0067810A1 (fr) 1982-12-29
AU7172781A (en) 1982-07-20

Similar Documents

Publication Publication Date Title
US4286330A (en) Autonomic string-manipulation system
US4994982A (en) Neural network system and circuit for use therein
US20190180188A1 (en) Evolution of Architectures For Multitask Neural Networks
Della Croce et al. A genetic algorithm for the job shop problem
Coello et al. Using genetic algorithms to design combinational logic circuits
Winfree Whiplash PCR for O (1) computing
Agranat et al. A CCD based neural network integrated circuit with 64K analog programmable synapses
Grzebyk et al. On identification of multi‐factor models with correlated residuals
Searls Formal language theory and biological macromolecules.
WO1982002267A1 (fr) Systeme de manipulation de chaines autonome
Cavaliere et al. Multiset random context grammars, checkers, and transducers
Alhazov et al. P systems with activation and blocking of rules
US6124444A (en) DNA sequences useful for computation
Myoupo et al. Time-efficient parallel algorithms for the longest common subsequence and related problems
Lendaris et al. Improved generalization in ANNs via use of conceptual graphs: a character recognition task as an example case
Martinez An automaton analogue of unicellularity
Moraal Graph-theoretical characterization of invertible cellular automata
Yang et al. Revisit of a Diaconis urn model
Kim Operators by Computational Learning
Ghuman et al. Improved online algorithms for jumbled matching
Damaschke Incremental haplotype inference, phylogeny and almost bipartite graphs
Hayes On the finite-state machine, a minimal model ofmousetraps, ribosomes and the human soul
Flanders Coroutines in Pascal
Regan A new parallel vector model, with exact characterization of NC k
Tongyu Implementation of suffix trees using two linear time algorithms and their application to string matching

Legal Events

Date Code Title Description
AK Designated states

Designated state(s): AU BR DK JP SU

AL Designated countries for regional patents

Designated state(s): AT CH DE FR GB NL SE

WWP Wipo information: published in national office

Ref document number: 1981901382

Country of ref document: EP

WWE Wipo information: entry into national phase

Ref document number: 1981901382

Country of ref document: EP

WWW Wipo information: withdrawn in national office

Ref document number: 1981901382

Country of ref document: EP