Models of massive parallelism: analysis of cellular automata and neural networks ; with ... 10 tables
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1995
|
| Series: | Texts in theoretical computer science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Litaraturangaben |
| Physical Description: | XIV, 272 S. graph. Darst. |
| ISBN: | 3540561498 0387561498 |
Staff View
MARC
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| 100 | 1 | |a Garzon, Max |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Models of massive parallelism |b analysis of cellular automata and neural networks ; with ... 10 tables |c Max Garzon |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1995 | |
| 300 | |a XIV, 272 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Texts in theoretical computer science | |
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Record in the Search Index
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| adam_text |
TABLE
OF
CONTENTS
1.
TURING
COMPUTABILITY
AND
COMPLEXITY
.
1
1.1
MODELS
OF
SEQUENTIAL
COMPUTATION
.
2
1.1.1
A
SIMPLE
MODEL:
THE
FINITE-STATE
MACHINE
.
3
1.1.2
TURING
MACHINES
.
7
1.2
COMPLEXITY
.
8
1.2.1
NONDETERMINISTIC
COMPUTATIONS
.
10
1.2.2
RANDOMIZED
ALGORITHMS
.
11
1.2.3
PARALLEL
COMPUTATION
.
13
1.3
CELLULAR
MACHINES
.
13
1.4
PREREQUISITES
.
14
REFERENCES
.
15
2.
CELLULAR
AUTOMATA
.
17
2.1
FINITE-STATE
AUTOMATA
.
17
2.2
REGULAR
GRAPHS
.
20
2.3
LOCAL
RULES
AND
GLOBAL
MAPS
.
22
2.3.1
CELLULAR
SPACES
.
23
2.3.2
LOCAL
RULES
.
25
2.3.3
GLOBAL
MAPS
AND
DYNAMICAL
SYSTEMS
.
27
2.4
FUNDAMENTAL
QUESTIONS
.
28
2.5
NOTATION
.
31
2.6
PROBLEMS
.
32
2.7
NOTES
.
35
REFERENCES
.
37
3.
LINEAR
CELLULAR
AUTOMATA
.
39
3.1
LINEAR
RULES
.
39
3.2
BASIC
PROPERTIES
.
41
3.2.1
GLOBAL
INJECTIVITY
AND
SURJECTIVITY
MODULO
M
.
42
3.2.2
SELF-REPRODUCTION
WITH
LINEAR
AUTOMATA
.
47
3.2.3
LINEAR
AUTOMATA
ON
RINGS
AND
SEMIGROUPS
.
47
3.3
GLOBAL
DYNAMICS
VIA
FRACTALS
.
YY.
49
3.4
THE
ROLE
OF
LINEAR
RULES
.
54
3.5
'
PROBLEMS
.
55
3.6
NOTES
.
59
REFERENCES
.
60
XII
TABLE
OF
CONTENTS
4.
SEMI-TOTALISTIC
AUTOMATA
.
63
4.1
SEMI-TOTALISTIC
RULES
.
63
4.1.1
AN
EXAMPLE:
CONWAY
'
S
GAME
OF
LIFE
.
64
4.1.2
NOMENCLATURE
FOR
TOTALISTIC
RULES
.
64
4.2
CONSTRUCTION
AND
COMPUTATION
UNIVERSALITY
.
65
4.2.1
COMPUTATION
UNIVERSALITY
OF
LIFE
.
66
4.2.2
CONSTRUCTIBILITY
AND
SELF-REPRODUCTION
.
67
4.2.3
PROVABLE
COMPUTATION
UNIVERSALITY
.
70
4.3
RESTRICTED
TOTALISTIC
RULES
.
YY
.
72
4.4
THRESHOLD
AUTOMATA
.
74
4.5
PROBLEMS
.
75
4.6
NOTES
.
76
REFERENCES
.
77
5.
DECISION
PROBLEMS
.
79
5.1
ALGORITHMIC
AND
DYNETIC
PROBLEMS
.
79
5.2
ID
EUCLIDEAN
AUTOMATA
.
82
5.3
2D
EUCLIDEAN
AUTOMATA
.
84
5.3.1
REVERSIBILITY
IS
UNSOLVABLE
.
85
5.3.2
SURJECTIVITY
IS
UNSOLVABLE
.
86
5.4
NONEUCLIDEAN
AUTOMATA
.
87
5.5
COMPLEXITY
QUESTIONS
.
89
5.6
PROBLEMS
.
91
5.7
NOTES
.
93
REFERENCES
.
94
6.
NEURAL
AND
RANDOM
BOOLEAN
NETWORKS
.
97
6.1
TYPES
OF
GENERALIZATIONS
.
97
6.2
OTHER
PARALLEL
MODELS
.
100
6.3
SUMMARY
OF
RESULTS
.
102
6.4
PROOFS
.
106
6.4.1
A
HIERARCHY
.
106
6.4.2
A
UNIVERSAL
NEURAL
NETWORK
.
109
6.4.3
EQUIVALENCE
OF
CELLULAR
AUTOMATA
AND
NEURAL
NETWORKS
.
ILL
6.4.4
EQUIVALENCE
OF
NEURAL
NETWORKS
AND
RANDOM
NETWORKS
.
ILL
6.4.5
THE
STABILITY
PROBLEM
IS
NEURALLY
UNSOLVABLE
.
112
6.5
PROBLEMS
.
113
6.6
NOTES
.
113
REFERENCES
.
115
7.
GENERAL
PROPERTIES
.
117
7.1
METRIC
PRELIMINARIES
.
118
7.1.1
METRICS
AND
TOPOLOGIES
.
118
7.1.2
CONVERGENCE
AND
CONTINUITY
.
120
7.2
BASIC
RESULTS
.
121
7.2.1
THE
MOORE-MYHILL
THEOREM
.
122
7.2.2
NONDETERMINISTIC
CELLULAR
AUTOMATA
.
126
TABLE
OF
CONTENTS
XIII
7.3
INJECTIVITY,
SURJECTIVITY
AND
LOCAL
REVERSIBILITY
.
130
7.4
SOME
GENERALIZATIONS
.
131
7.4.1
NEURAL
AND
RANDOM
NETWORKS
.
131
7.4.2
COMBINATORIAL
GENERALIZATIONS
ON
EUCLIDEAN
SPACES
.
134
7.5
PROBLEMS
.
135
7.6
NOTES
.
137
REFERENCES
.
138
8.
CLASSIFICATION
.
141
8.1
FINITE
NETWORKS
.
142
8.1.1
THE
DIFFICULTIES
.
143
8.1.2
COMPLEXITY
OF
CLASSIFYING
FINITE
NETWORKS
.
144
8.2
WOLFRAM
CLASSIFICATION
.
147
8.3
CLASSIFICATION
VIA
LIMIT
SETS
.
149
8.3.1
CULIK-YU
'
S
CLASSES
AND
ISHII
'
S
CLASSES
.
149
8.3.2
ABOUT
ENTROPY
.
151
8.4
MEAN
FIELD
THEORY
.
153
8.5
LOCAL
STRUCTURE
THEORY
.
156
8.5.1
ZEROTH-ORDER
AND
FIRST-ORDER
LOCAL
STRUCTURE
THEORIES
.
157
8.5.2
HIGHER-ORDER
LOCAL
STRUCTURE
THEORIES
.
158
8.6
OTHER
CLASSIFICATIONS
.
158
8.7
PROBLEMS
.
161
8.8
NOTES
.
163
REFERENCES
.
165
9.
ASYMPTOTIC
BEHAVIOR
.
167
9.1
LINEAR
RULES
.
167
9.1.1
LINEAR
AUTOMATA
ON
TORI
.
167
9.1.2
LINEAR
AUTOMATA
ON
THE
LINE
.
170
9.2
EXACT
SOLUTION
.
171
9.3
SIMULATION
IN
CONTINUOUS
SYSTEMS
.
173
9.3.1
DISCRETE
COMPUTATION
BY
CONTINUOUS
SYSTEMS
.
173
9.3.2
NONLOCAL
PROPERTIES
.
176
9.3.2.1
THE
^-TRANSFORM
.
177
9.3.2.2
SARKOVSKII
'
S
THEOREM
.
.
.
181
9.4
OBSERVABILITY
.
184
9.4.1
OBSERVABILITY
OF
THE
IDENTITY
.
185
9.4.2
TOGGLE
RULES
AND
THE
EXTENSION
PROPERTY
.
186
9.4.3
OBSERVABILITY
OF
LINEAR
CELLULAR
AUTOMATA
.
188
9.4.4
OBSERVABILITY
IN
NEURAL
NETWORKS
.
190
9.5
PROBLEMS
.
192
9.6
NOTES
.
194
REFERENCES
.
196
10.
SOME
INVERSE
PROBLEMS
.
199
10.1
SIGNALS
AND
SYNCHRONIZATION
.
200
10.1.1
SYNCHRONIZATION
OF
A
LINE
.
200
XIV
TABLE
OF
CONTENTS
10.1.2
SYNCHRONIZATION
OF
A
NETWORK
.
204
10.1.3
SIGNALS
IN
DIMENSION
1
.
204
10.1.4
CLOCKS
.
206
10.2
FORMAL
LANGUAGE
RECOGNITION
.
209
10.2.1
MODELS
.
209
10.2.2
A
SPEEDUP
THEOREM
.
212
10.3
PICTURE
LANGUAGES
.
213
10.3.1
THE
ISSUE
OF
REPRESENTATION
.
214
10.3.2
7R-LANGUAGES
IN
SPACES
OF
LINEAR
GROWTH
.
215
10.3.3
2D-EUCLIDEAN
LANGUAGES
.
216
10.3.4
RECOGNITION
OVER
SPACES
OF
EXPONENTIAL
GROWTH
.
218
10.3.5
RECOGNITION
OVER
SPACES
OF
SUBEXPONENTIAL
GROWTH
.
220
10.4
PROBLEMS
.
223
10.5
NOTES
.
225
REFERENCES
.
226
11.
REAL
COMPUTATION
.
231
11.1
REPRESENTATION
AND
PRIMITIVES
.
232
11.2
EXACT
COMPUTATION
.
234
11.2.1
CONSTANT-TIME
COMPUTATION
.
234
11.2.2
VARIABLE-TIME
COMPUTATION
.
237
11.3
APPROXIMATE
COMPUTATION
BY
NEURAL
NETS
.
239
11.3.1
RELATIVE
SHADOWING
.
239
11.3.2
SHADOWING
BASES
.
244
11.4
PROBLEMS
.
250
11.5
NOTES
.
251
REFERENCES
.
253
12.
A
BIBLIOGRAPHY
OF
APPLICATIONS
.
255
12.1
PHYSICS
.
255
12.2
CHEMISTRY
.
255
12.3
BIOLOGY
.
256
12.4
COMPUTER
SCIENCE
.
256
12.5
ARTIFICIAL
INTELLIGENCE
AND
COGNITIVE
SCIENCE
.
257
12.6
MISCELLANEOUS
.
257
REFERENCES
.
258
AUTHOR
INDEX
.
263
SYMBOL
INDEX
.
267
SUBJECT
INDEX
.
269 |
| any_adam_object | 1 |
| author | Garzon, Max |
| author_facet | Garzon, Max |
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| ctrlnum | (OCoLC)246709926 (DE-599)BVBBV010172542 |
| dewey-full | 004/.35 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 004 - Computer science |
| dewey-raw | 004/.35 |
| dewey-search | 004/.35 |
| dewey-sort | 14 235 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV010172542 |
| illustrated | Illustrated |
| indexdate | 2024-08-19T00:33:39Z |
| institution | BVB |
| isbn | 3540561498 0387561498 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006756797 |
| oclc_num | 246709926 |
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| physical | XIV, 272 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series2 | Texts in theoretical computer science |
| spelling | Garzon, Max Verfasser aut Models of massive parallelism analysis of cellular automata and neural networks ; with ... 10 tables Max Garzon Berlin [u.a.] Springer 1995 XIV, 272 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in theoretical computer science Litaraturangaben Zellularer Automat (DE-588)4190671-8 gnd rswk-swf Neuronales Netz (DE-588)4226127-2 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Zellularer Automat (DE-588)4190671-8 s DE-604 Neuronales Netz (DE-588)4226127-2 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006756797&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Garzon, Max Models of massive parallelism analysis of cellular automata and neural networks ; with ... 10 tables Zellularer Automat (DE-588)4190671-8 gnd Neuronales Netz (DE-588)4226127-2 gnd |
| subject_GND | (DE-588)4190671-8 (DE-588)4226127-2 (DE-588)4143413-4 |
| title | Models of massive parallelism analysis of cellular automata and neural networks ; with ... 10 tables |
| title_auth | Models of massive parallelism analysis of cellular automata and neural networks ; with ... 10 tables |
| title_exact_search | Models of massive parallelism analysis of cellular automata and neural networks ; with ... 10 tables |
| title_full | Models of massive parallelism analysis of cellular automata and neural networks ; with ... 10 tables Max Garzon |
| title_fullStr | Models of massive parallelism analysis of cellular automata and neural networks ; with ... 10 tables Max Garzon |
| title_full_unstemmed | Models of massive parallelism analysis of cellular automata and neural networks ; with ... 10 tables Max Garzon |
| title_short | Models of massive parallelism |
| title_sort | models of massive parallelism analysis of cellular automata and neural networks with 10 tables |
| title_sub | analysis of cellular automata and neural networks ; with ... 10 tables |
| topic | Zellularer Automat (DE-588)4190671-8 gnd Neuronales Netz (DE-588)4226127-2 gnd |
| topic_facet | Zellularer Automat Neuronales Netz Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006756797&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT garzonmax modelsofmassiveparallelismanalysisofcellularautomataandneuralnetworkswith10tables |