LG: New Technology for Military Applications - iaria.org · Mikhail Botvinnik . 1911 - 1995. 6th...
Transcript of LG: New Technology for Military Applications - iaria.org · Mikhail Botvinnik . 1911 - 1995. 6th...
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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.
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What is Linguistic Geometry?
John von Neumann
Mikhail Botvinnik
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Claude Shannon 1950
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A Comparison of Searches for the same processing time
Brute Force Search
Alpha-Beta Search
Human Expert Search and LG Search
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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
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Mikhail Botvinnik
1911 - 1995 6th World Champion
1948 - 1957, 1958 - 1960, 1961 - 1963
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Mikhail Botvinnik "To Achieve the Goal"
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Moscow State
University
1972
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M. Botvinnik
A Flow Chart of The Algorithm for
Playing Chess
1972
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1977
Program PIONEER
Nadareishvili Endgame
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Program PIONEER
Nadareishvili Endgame
First Winning Strategies
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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
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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
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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
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First Hierarchy
of Languages, a predecessor of LG
1981- 1985
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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
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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
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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
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The Arts Building is framed by fall leaves.
1990-91 McGill University
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From 2D to 3D Models
12345678
1 2 3 4 5 6 7 8
1
234
5678
xy
z
1993
First 3D Board
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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
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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
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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
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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
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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
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• 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
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1999
9/9/99 Denver, CO
www.stilman-strategies.com
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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
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2004-08 DARPA RAID Experiments
Validation of MOUT Strategies: Competition with People
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• 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
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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