lg: new technology for military 2016-09-11آ  mikhail botvinnik . 1911 - 1995. 6th world champion...

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  • Linguistic Geometry: Adversarial Reasoning for Real Life

    Problems

    Boris Stilman University of Colorado Denver, USA STILMAN Advanced Strategies, USA

    Copyright © 2011 STILMAN Advanced Strategies, LLC. All rights reserved. All other

    names, pictures and data where referenced are trademarks or property of their respective owners.

  • What is Linguistic Geometry?

    John von Neumann

    Mikhail Botvinnik

  • Claude Shannon 1950

  • A Comparison of Searches for the same processing time

    Brute Force Search

    Alpha-Beta Search

    Human Expert Search and LG Search

  • 1997

    Rematch Garry Kasparov

    vs Deep Blue

    Facts Garry Kasparov IBM's Deep Blue

    Height: Weight: Age: Birthplace: # Processors: Moves/Second: Power Source: Next Career:

    5'10" 176 lbs. 34 years Azerbaijan 100B Neurons 2 electrical/chemical champion

    6'5" 1.4 tons 4 years Yorktown, NY 32 P2SC Processors 200 million electrical none

  • Mikhail Botvinnik

    1911 - 1995 6th World Champion

    1948 - 1957, 1958 - 1960, 1961 - 1963

  • Mikhail Botvinnik "To Achieve the Goal"

  • Moscow State

    University

    1972

  • M. Botvinnik

    A Flow Chart of The Algorithm for

    Playing Chess

    1972

  • 1977

     Program PIONEER

    Nadareishvili Endgame

  •  Program PIONEER

    Nadareishvili Endgame

    First Winning Strategies

  • Ba3 Q:a3 Nh5+ P:h5 Qg5+ Kh8 e7 Qc1+ Kf2Q:f5+ Kg8

    Qd2+ Kg3 Qe3+ Kh4 Qe1+ K:h5 Qe2+ Kh4 Qe1+ Kh3 Qe3+ Pg3 +100

    Q:c3 Pg3

    +100 Qe4+ Kh3 Qe3+

    Qd3+ Pg3 +100

    +100

    Qd1+ Pg4 +100

    +100

    Qe4+ K:h5 Qg6+ Q:g6+ Ph:g+ K:g6

    +100 Qe2+

    Moscow, USSR

    Program PIONEER

    1 2 3 4 5 6 7 8

    a b c d e f g h

    +

    +

    ++

    1980

    First Strategies with Positional Sacrifices

  • 1

    3 4

    2

    q 2

    1

    3

    4

    p 22

    q

    Attack

    Block or Relocation

    1

    3

    4

    q

    p 22

    q2

    Domination

    q 0

    p 2

    q 1

    p 1

    p 0

    q 1

    p 0 q3

    Unblock

    Retreat

    q

    p 0 q3

    q 3

    q 1

    p 0

    2

    1

    p 1

    Types of Zones

     Zones

  • Abstract Board Games

    An Abstract Board Game is the following eight-tuple

    < X, P, Rp, {ON} , v, Si, St, TR>

    X = {xi} is a finite set of points; P = {pi} is a finite set of elements; P=P1 ∪ P2, P1 ∩ P2={ }; Rp(x, y) is a family of binary relations of reachability in X (x ∈ X, y ∈ Y, p ∈ P); y is reachable from x for p; ON(p) = x is a partial function of placement of elements P into X; v> 0 is a real function, v(pi) are the values of elements; Si is a set of initial states of the system, a certain set of formulas {ON(pi)=xi}; St is a set target states of the system (as Si); TR is a set of operators TRANSITION(p, x, y) for transition of the system from one state to another described as follows precondition: (ON(p) = x) ^ Rp(x, y) delete: ON(p) = x add: ON(p) = y

    1981

  • First Hierarchy

    of Languages, a predecessor of LG

    1981- 1985

  • a(f6)a(e5)a(e4)a(f3)a(g2)a(h1)

    1

    2

    3

    4

    5

    6

    7

    8

    a b c d e f g h

    1981

    Language of Trajectories

  • Z = t(po, a(1)a(2)a(3)a(4)a(5), 5)t(q3, a(6)a(7)a(4), 4)

    t(q2, a(8)a(9)a(4), 4)t(p1, a(13)a(9), 3) t(q1, a(11)a(12)a(9), 3)t(p2, a(10)a(12), 2)

    1

    2

    3

    4

    57

    6

    9 8

    10

    11

    13

    12

    q

    q

    q

    q

    p

    p p

    0

    1

    2

    2

    4 3

    1

    Language of Networks (Zones)

    1982

  • State S1

    2

    3

    4

    57

    6

    9

    10

    11

    13

    12

    q

    q

    q

    q

    p p

    14 16

    15

    18

    q

    p

    17

    5

    2

    13

    4

    0 2

    1

    1

    8

    State S2

    2

    3

    4

    57

    6

    9

    10

    11

    13

    12

    q

    q

    q

    q

    p p

    14 16

    15

    18

    q

    p

    17

    5

    2

    1

    3

    4

    0 2

    1

    1

    8

    2

    Language of Translations

    1982

  • The Arts Building is framed by fall leaves.

    1990-91 McGill University

  • From 2D to 3D Models

    12 34

    56 78

    1 2 3 4

    5 6 7 8

    1

    2 3 4

    5 6 7 8

    x y

    z

    1993

    First 3D Board

  • From Limited to n×n Variable Size District

    8 7 6 5 4 3 2 1

    2 1 3 4 5 6 7 8

    n

    n ...

    . . .

    1995

    First n×n Board

  • 8 7 6 5 4 3 2 1

    2 1345678

    n

    n ...

    ...

    63-62 83-72

    62-61 72-61 -1

    11-22

    72-61 12-13

    -162-61

    62-61 22-33

    13-14

    63-62 12-13 83-72

    -162-61 72-61

    62-61 22-33

    72-61 13-14 -1

    22-33

    -162-6133-44 14-15

    33-44

    12-13 62-61 22-33

    13-14

    83-72 22-13 62-61 72-61 0

    22-33

    62-61 53-52

    16-17

    83-72 62-61 72-61 -1

    11-12 62-61 72-61 -1

    11-22

    11-22 62-61 -1

    11-22 12-13

    -162-61

    62-61 14-15 -133-44 33-44

    -1

    44-53 15-16

    12-13

    72-61

    72-61 13-14

    13-14 14-15

    14-15

    13-14

    13-14

    13-14 22-33 -162-61

    62-61 -133-44 33-44 44-53 61-62

    14-15 15-16

    15-16

    15-16

    0

    12-13

    -113-14

    -1 62-61

    13-14 72-61 14-15

    14-15 62-61 53-52

    16-1744-53 15-16 0

    +1

    12-13

    -161-62

    44-35 61-62 0

    -115-16

    -161-62

    44-35 61-62 0

    -115-16

    44-35 61-62 -1

    11-22 12-13 83-72 22-33 33-44

    13-14 72-61 14-15 62-61

    53-52 16-17

    44-53 15-16

    0 63-62

    1995

    First Concurrent Strategies

  • Experiments with State Space Chart: NO-Search Approach

    WB-Intercept and BB-Protect

    W-Zone

    B-Zone

    WB-Protect and BB-Intercept

    W-Zone

    B-Zone

    WB-Protect and BB-Protect

    W-Zone

    B-Zone

    WB-Intercept and BB-Intercept

    W-Zone

    B-Zone

    Start State

    DRAW

    Black Wins

    White Wins

    DRAW

    1996

    First Proof of Strategies Optimality

  • Planning of Maintenance Planning of Power Units (0,0,p)

    1 (1,0,p)

    1 (2,0,p)

    1 (g,0,p)

    1

    p 1

    Q 11

    Q 21

    (1,1,r) (1,0,r) (2,1,r) (2,0,r) (3,1,r) (3,0,r)

    (1,0,q) (2,0,q) 1 1

    2 2 2 (1,0,q) (2,0,q) (3,0,q)

    (0,0,p) (1,0,p) (2,0,p) (g,0,p) 2 2 2 2

    (0,1,p) (1,1,p) (2,1,p) 2 2 2

    Q 12 22

    p 2

    Q Q 23

    P res 1

    P2 res

    P 3

    res

    q 2

    q1

    loss loss

    loss loss loss

    1997

    First Artificial Enemy in LG

  • 1 2 3 4

    5 6 7 8

    1 2 3 4 1

    2 3 4 5

    x y

    z

    n-1 n

    n-2

    n n-1 n-2

    .

    .

    Computational complexity of the

    specific classes of abstract board games is polynomial with respect to the length of the input.

    1999

    First Proof of Polynomial Run Time

  • • Linguistic Geometry (LG) is a new type of game theory; • LG replaces search by construction, making the games computationally tractable.

    Manuscript finished in 1999

    Published in 2000

  • 1999

    9/9/99 Denver, CO

    www.stilman-strategies.com

  • 12 34

    56 78

    1 2 3 4

    5 6 7 8

    1

    2 3 4

    5 6 7 8

    x y

    z

    How does it do it?

    12 34

    56 78

    1 2 3 4

    5 6 7 8

    1

    2 3 4

    5 6 7 8

    x y

    z

    12 34

    56 78

    1 2 3 4

    5 6 7 8

    1

    2 3 4

    5 6 7 8

    x y

    z

    12 34

    56 78

    1 2 3 4

    5 6 7 8

    1

    2 3 4

    5 6 7 8

    x y

    z

    12 34

    56 78

    1 2 3 4

    5 6 7 8

    1

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