Subrecursive programming systems: complexity & succinctness
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston u.a.
Birkhäuser
1994
|
| Schriftenreihe: | Progress in theoretical computer science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 252 S. |
| ISBN: | 0817637672 3764337672 |
Internformat
MARC
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| 100 | 1 | |a Royer, James S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Subrecursive programming systems |b complexity & succinctness |c James S. Royer ; John Case |
| 264 | 1 | |a Boston u.a. |b Birkhäuser |c 1994 | |
| 300 | |a VII, 252 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Progress in theoretical computer science | |
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| 700 | 1 | |a Case, John |d 1888-1969 |e Verfasser |0 (DE-588)100072283 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1807324083051823104 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
1
1.1
WHAT
THIS
BOOK
IS
ABOUT
.
1
1.1.1
SUBRECURSIVE
PROGRAMMING
SYSTEMS
.
1
1.1.2
RELATIVE
SUCCINCTNESS
TRADE-OFFS
.
2
1.1.3
THE
TOOLKIT
.
5
1.2
OUTLINE
OF
PART
I.
A
SUBRECURSION
PROGRAMMING
SYSTEMS
TOOLKIT
.
7
1.3
OUTLINE
OF
PART
II.
PROGRAM
SUCCINCTNESS
.
11
1.4
BRIEF
HISTORY
OF
PRIOR
RESULTS
.
15
1.5
HOW
TO
USE
THIS
BOOK
.
17
1.6
ACKNOWLEDGMENTS
.
17
I
A
SUBRECURSION
PROGRAMMING
SYSTEMS
TOOLKIT
19
2
BASIC
NOTATION
AND
DEFINITIONS
21
2.1
EQUATION
NUMBERING
.
21
2.2
GENERAL
NOTATION
AND
CONVENTIONS
.
21
2.3
THE
STANDARD
PAIRING
FUNCTION
.
23
2.4
REPRESENTING
NUMBERS
.
24
2.5
OF
LENGTHS
AND
LOGARITHMS
.
25
2.6
CLASSES
OF
SETS
AND
FUNCTIONS
.
26
2.7
PROGRAMMING
SYSTEMS
AND
NUMBERINGS
.
26
2.8
COMPLEXITY
MEASURES
.
28
2.9
THE
ARITHMETIC
HIERARCHY
.
29
2.10
FORMAL
SYSTEMS
.
30
3
DETERMINISTIC
MULTI-TAPE
TURING
MACHINES
31
3.1
DETAILS
OF
THE
MODEL
.
31
3.1.1
TM
CONVENTIONS
.
31
3.1.2
CODING
TMS
.
33
3.1.3
THE
STANDARD
ACCEPTABLE
PROGRAMMING
SYSTEM
AND
COMPLEXITY
MEASURES
.
34
3.1.4
THE
COMPLEXITY
OF
BASIC
FUNCTIONS
AND
OPERATIONS
.
35
VI
CONTENTS
3.1.5
STANDARD
COMPLEXITY
CLASSES
.
39
3.1.6
EFFICIENT
UNIVERSAL
SIMULATION
.
40
3.2
COSTS
OF
COMBINING
TURING
MACHINES
AND
EFFICIENCY
OF
THE
COMBINATIONS
.
45
3.2.1
TM
NORMALIZATION
.
45
3.2.2
CLOCKED
TMS
.
47
3.2.3
COMBINING
TMS
.
50
3.2.4
SLOWED
SIMULATIONS
.
54
4
PROGRAMMING
SYSTEMS
56
4.1
CLOSURE
PROPERTIES
AND
CONTROL
STRUCTURES
.
56
4.1.1
FORMALIZING
THE
NOTION
OF
A
CONTROL
STRUCTURE
.
56
4.1.2
BUILDING
CONTROL
STRUCTURES
.
59
4.2
CLOCKED
PROGRAMMING
SYSTEMS
.
64
4.2.1
FORMALIZATIONS
.
65
4.2.2
CONSTRUCTING
CLOCKED
SYSTEMS
.
68
4.2.3
INHERITED
PROPERTIES
OF
CLOCKED
SYSTEMS
.
72
4.2.4
CLOCKED
SYSTEMS
FOR
COLLECTIONS
OF
SETS
.
75
4.3
PROVABLY
BOUNDED
PROGRAMMING
SYSTEMS
.
76
4.3.1
PROVABLY
EXPLICITLY
BOUNDED
SYSTEMS
.
76
4.3.2
PROVABLY
IMPLICITLY
BOUNDED
SYSTEMS
.
82
4.4
REDUCIBILITY
INDUCED
PROGRAMMING
SYSTEMS
.
86
4.4.1
INDUCED
SYSTEMS
AND
THEIR
PROPERTIES
.
87
4.4.2
THE
GENERALITY
OF
INDUCED
SYSTEMS
.
89
5
THE
LOOP
HIERARCHY
95
6
THE
POLY-DEGREE
HIERARCHY
105
7
DELAYED
ENUMERATION
AND
LIMITING
RECURSION
113
7.1
UNIFORM
ENUMERATIONS
.
114
7.2
LIMITING
RECURSION
.
118
7.3
UNIFORM
LIMITS
.
119
8
INSEPARABILITY
NOTIONS
122
8.1
PRODUCTIVENESS
AND
RELATED
NOTIONS
.
123
8.2
AN-INSEPARABILITY
.
123
8.3
E
N
-INSEPARABILITY
.
125
9
TOOLKIT
DEMONSTRATIONS
128
9.1
UNIFORM
DENSITY
.
129
9.2
A
GENERALIZATION
OF
UNIFORM
DENSITY
.
133
9.3
UPPER
BOUNDS
ON
UPWARD
CHAINS
.
137
9.4
MINIMAL
PAIRS
.
142
9.5
SUFFICIENT
CONDITIONS
FOR
EFFECTIVE
E2-INSEPARABILITY
.
148
CONTENTS
VII
II
PROGRAM
SUCCINCTNESS
153
10
NOTIONS
OF
SUCCINCTNESS
155
10.1
PROGRAM
SIZE
.
155
10.2
RELATIVE
SUCCINCTNESS:
DEFINITIONS
.
155
10.3
INVARIANCES
AND
LIMITATIONS
.
158
10.3.1
INVARIANCE
WITH
RESPECT
TO
PROGRAM
SIZE
MEASURES
.
158
10.3.2
LIMITS
ON
SUCCINCTNESS
.
159
10.3.3
INVARIANCE
UNDER
CHOICE
OF
PROGRAMMING
SYSTEMS
.
160
10.3.4
PROGRAMMING
SYSTEMS
THAT
REPRESENT
CLASSES
OF
SETS
161
11
LIMITING-RECURSIVE
SUCCINCTNESS
PROGRESSIONS
162
11.1
A
TECHNICAL
PRELUDE
.
162
11.2
THE
KEY
THEOREM
.
167
11.3
A
CORNUCOPIA
OF
COROLLARIES
.
171
11.4
A
TIGHT
INCOMPLETENESS
THEOREM
ABOUT
COMPLEXITY
BOUNDS
182
11.5
CHARACTERIZATIONS
OF
LIMITING-RECURSIVE
SUCCINCTNESS
.
185
12
SUCCINCTNESS
FOR
FINITE
AND
INFINITE
VARIANTS
191
12.1
THE
=
M
CASE
.
191
12.2
CONSIDERATIONS
FOR
THE
=*
AND
=
CASES
.
192
12.3
THE
=*
CASE
.
194
12.4
THE
=
CASE
.
197
13
SUCCINCTNESS
FOR
SINGLETON
SETS
200
13.1
PROGRESSIONS
FOR
CLOCKED
SYSTEMS
.
200
13.2
SUCCINCTNESS
FOR
PROGRAMS
WITH
PROVABLE
COMPLEXITY
.
215
14
FURTHER
PROBLEMS
221
APPENDIX
A
EXERCISES
223
APPENDIX
B
SOLUTIONS
FOR
SELECTED
EXERCISES
234
BIBLIOGRAPHY
239
NOTATION
INDEX
247
SUBJECT
INDEX
249 |
| any_adam_object | 1 |
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| indexdate | 2024-08-14T01:22:38Z |
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| language | English |
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| spelling | Royer, James S. Verfasser aut Subrecursive programming systems complexity & succinctness James S. Royer ; John Case Boston u.a. Birkhäuser 1994 VII, 252 S. txt rdacontent n rdamedia nc rdacarrier Progress in theoretical computer science Computer programming Programmierlogik (DE-588)4047408-2 gnd rswk-swf Rekursives Programmschema (DE-588)4300728-4 gnd rswk-swf Programmierlogik (DE-588)4047408-2 s DE-604 Rekursives Programmschema (DE-588)4300728-4 s Case, John 1888-1969 Verfasser (DE-588)100072283 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006556487&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Royer, James S. Case, John 1888-1969 Subrecursive programming systems complexity & succinctness Computer programming Programmierlogik (DE-588)4047408-2 gnd Rekursives Programmschema (DE-588)4300728-4 gnd |
| subject_GND | (DE-588)4047408-2 (DE-588)4300728-4 |
| title | Subrecursive programming systems complexity & succinctness |
| title_auth | Subrecursive programming systems complexity & succinctness |
| title_exact_search | Subrecursive programming systems complexity & succinctness |
| title_full | Subrecursive programming systems complexity & succinctness James S. Royer ; John Case |
| title_fullStr | Subrecursive programming systems complexity & succinctness James S. Royer ; John Case |
| title_full_unstemmed | Subrecursive programming systems complexity & succinctness James S. Royer ; John Case |
| title_short | Subrecursive programming systems |
| title_sort | subrecursive programming systems complexity succinctness |
| title_sub | complexity & succinctness |
| topic | Computer programming Programmierlogik (DE-588)4047408-2 gnd Rekursives Programmschema (DE-588)4300728-4 gnd |
| topic_facet | Computer programming Programmierlogik Rekursives Programmschema |
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