lg: new technology for military applications · 2016-09-11 · mikhail botvinnik . 1911 - 1995. 6th...
TRANSCRIPT
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
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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
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1 2 3 4 5 6 7 8
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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
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How does it do it?
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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