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

+100Qe4+ Kh3 Qe3+

Qd3+ Pg3+100

+100

Qd1+ Pg4 +100

+100

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

+100Qe2+

Moscow, USSR

Program PIONEER

12345678

a b c d e f g h

+

+

++

1980

First Strategies with Positional Sacrifices

1

34

2

q2

1

3

4

p22

q

Attack

Block or Relocation

1

3

4

q

p22

q2

Domination

q0

p2

q1

p1

p0

q1

p0 q3

Unblock

Retreat

q

p0 q3

q3

q1

p0

2

1

p1

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

43

1

Language of Networks (Zones)

1982

State S1

2

3

4

57

6

9

10

11

13

12

q

q

q

q

pp

14 16

15

18

q

p

17

5

2

13

4

02

1

1

8

State S2

2

3

4

57

6

9

10

11

13

12

q

q

q

q

pp

14 16

15

18

q

p

17

5

2

1

3

4

02

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

12345678

1 2 3 4 5 6 7 8

1

234

5678

xy

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

87654321

2 1345678

n

n ...

...

63-62 83-72

62-61 72-61-1

11-22

72-6112-13

-162-61

62-6122-33

13-14

63-6212-1383-72

-162-61 72-61

62-6122-33

72-6113-14 -1

22-33

-162-6133-44

14-15

33-44

12-13 62-6122-33

13-14

83-72 22-1362-61 72-61 0

22-33

62-6153-52

16-17

83-72 62-61 72-61-1

11-1262-61 72-61 -1

11-22

11-2262-61 -1

11-2212-13

-162-61

62-61 14-15 -133-4433-44

-1

44-53 15-16

12-13

72-61

72-61 13-14

13-14 14-15

14-15

13-14

13-14

13-1422-33 -162-61

62-61 -133-4433-44 44-53 61-62

14-15 15-16

15-16

15-16

0

12-13

-113-14

-162-61

13-1472-61 14-15

14-15 62-6153-52

16-1744-53 15-160

+1

12-13

-161-62

44-35 61-620

-115-16

-161-62

44-35 61-620

-115-16

44-35 61-62-1

11-22 12-1383-72 22-33 33-44

13-1472-61 14-15 62-61

53-5216-17

44-5315-16

063-62

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

BlackWins

WhiteWins

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

p1

Q11

Q21

(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

Q12 22

p2

Q Q23

Pres1

P2

resP

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

12345678

1 2 3 4 5 6 7 8

1

234

5678

xy

z

How does it do it?

12345678

1 2 3 4 5 6 7 8

1

234

5678

xy

z

12345678

1 2 3 4 5 6 7 8

1

234

5678

xy

z

12345678

1 2 3 4 5 6 7 8

1

234

5678

xy

z

12345678

1 2 3 4 5 6 7 8

1

234

5678

xy

z

12345678

1 2 3 4 5 6 7 8

1

234

5678

xy

z

12345678

1 2 3 4 5 6 7 8

1

234

5678

xy

z

12345678

1 2 3 4 5 6 7 8

1

234

5678

xy

z

12345678

1 2 3 4 5 6 7 8

1

234

5678

xy

z

12345678

1 2 3 4 5 6 7 8

1

234

5678

xy

z

12345678

1 2 3 4 5 6 7 8

1

234

5678

xy

z

DARPA JFACC Experiments 1999 – 2001

Validation of SEAD Strategies: Expert Opinions

2004-08 DARPA RAID Experiments

Validation of MOUT Strategies: Competition with People

• Chess Masters’ Problem Solving • Search Reduction Techniques • Subclass of Gaming Problems of Polynomial Complexity • No-Search Paradigm for Decision Making: “From Search to Construction” • OR maybe, it is something else . . .

What is Linguistic Geometry? John von Neumann

Mikhail Botvinnik

It appears that LG is a model of human thinking about conflict resolution, a warfighting model at the level of superintelligence . . .

John von Neumann

Mikhail Botvinnik