Computability, complexity, and languages: fundamentals of theoretical computer science
Gespeichert in:
Hauptverfasser: | , , |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
San Diego, Calif. [u.a.]
Acad. Press
1994
|
Ausgabe: | 2. ed. |
Schriftenreihe: | Computer science and scientific computing
|
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis Klappentext |
Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
Beschreibung: | XIX, 609 S. graph. Darst. |
ISBN: | 0122063821 |
Internformat
MARC
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100 | 1 | |a Davis, Martin |d 1928-2023 |e Verfasser |0 (DE-588)116040866 |4 aut | |
245 | 1 | 0 | |a Computability, complexity, and languages |b fundamentals of theoretical computer science |c Martin D. Davis ; Ron Sigal ; Elaine J. Weyuker |
250 | |a 2. ed. | ||
264 | 1 | |a San Diego, Calif. [u.a.] |b Acad. Press |c 1994 | |
300 | |a XIX, 609 S. |b graph. Darst. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 0 | |a Computer science and scientific computing | |
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Datensatz im Suchindex
_version_ | 1804124099408035840 |
---|---|
adam_text | Contents
Preface
xiii
Acknowledgments
xvii
Dependency Graph
xix
1
Preliminaries
1
1.
Sets and
л
-tuples
1
2.
Functions
3
3.
Alphabets and Strings
4
4.
Predicates
5
5.
Quantifiers
6
6.
Proof by Contradiction
8
7.
Mathematical Induction
9
Part
1
Computability
15
2
Programs and Computable Functions
17
1.
A Programming Language
17
2.
Some Examples of Programs
18
3.
Syntax
25
4.
Computable Functions
28
5.
More about Macros
32
vii
viti
Contents
3
Primitive
Recursive Functions
39
1.
Composition
39
2.
Recursion
40
3.
PRC Classes
42
4.
Some Primitive Recursive Functions
44
5.
Primitive Recursive Predicates
49
6.
Iterated Operations and Bounded Quantifiers
52
7.
Minimalization
55
8.
Pairing Functions and
Godei
Numbers
59
4
A Universal Program
65
1.
Coding Programs by Numbers
65
2.
The Halting Problem
68
3.
Universality
70
4.
Recursively Enumerable Sets
78
5.
The Parameter Theorem
85
6.
Diagonalization and Reducibility
88
7.
Rice s Theorem
95
*8. The Recursion Theorem
97
*9. A Computable Function That Is Not Primitive Recursive
105
5
Calculations on Strings
113
1.
Numerical Representation of Strings
113
2.
A Programming Language for String Computations
121
3.
The Languages
«У
and ¿rn
126
4.
Post
-Tu
ring Programs
129
5.
Simulation of S^ ¡n
& 135
6.
Simulation of ¿/ in
¿Ѓ
140
6
Turing Machines
145
1.
Internal States
145
2.
A Universal Turing Machine
152
3.
The Languages Accepted by Turing Machines
153
4.
The Halting Problem for Turing Machines
157
5.
Nondeterministic Turing Machines
159
6.
Variations on the Turing Machine Theme
162
7
Processes and Grammars
169
1.
Semi-Thue Processes
169
2.
Simulation of Nondeterministic Turing Machines by
Semi-Thue Processes
171
Contents ix
3. Unsolvable Word Problems 176
4.
Post s Correspondence
Problem 181
5. Grammars 186
6.
Some
Unsolvable Problems
Concerning Grammars
191
*7. Normal
Processes
192
8
Classifying
Unsolvable Problems 197
1.
Using
Oracles 197
2. Relativization
of Universality
201
3.
Reducibility
207
4. Sets r.e. Relative
to an
Oracle 211
5.
The Arithmetic Hierarchy
215
6.
Post s
Theorem 217
7.
Classifying Some Unsolvable Problems
224
8.
Rice s Theorem Revisited
230
9.
Recursive Permutations
231
Part
2
Grammars and Automata
235
9
Regular Languages
237
1.
Finite Automata
237
2.
Nondeterministic Finite Automata
242
3.
Additional Examples
247
4.
Closure Properties
249
5.
Kleene s Theorem
253
6.
The Pumping Lemma and Its Applications
260
7.
The Myhill-Nerode Theorem
263
10
Context-Free Languages
269
1.
Context-Free Grammars and Their Derivation Trees
269
2.
Regular Grammars
280
3.
Chomsky Normal Form
285
4.
Ваг
-Hilleľs
Pumping Lemma
287
5.
Closure Properties
291
*6. Solvable and Unsolvable Problems
297
7.
Bracket Languages
301
8.
Pushdown Automata
308
9.
Compilers and Formal Languages
323
χ
Contents
11
Context-Sensitive Languages
327
1.
The Chomsky Hierarchy
327
2.
Linear Bounded Automata
330
3.
Closure Properties
337
Part
3
Logic
345
12
Propositional Calculus
347
1.
Formulas and Assignments
347
2.
Tautological Inference
352
3.
Normal Forms
353
4.
The Davis-Putnam Rules
360
5.
Minimal Unsatisfiability and Subsumption
366
6.
Resolution
367
7.
The Compactness Theorem
370
13
Quantification Theory
375
1.
The Language of Predicate Logic
375
2.
Semantics
377
3.
Logical Consequence
382
4.
Herbrand s Theorem
388
5.
Unification
399
6.
Compactness and Countability
404
*7.
Godeľs
Incompleteness Theorem
407
*8. Unsolvability of the Satisfiability Problem in Predicate Logic
410
Part
4
Complexity
417
14
Abstract Complexity
419
1.
The Blum Axioms
419
2.
The Gap Theorem
425
3.
Preliminary Form of the Speedup Theorem
428
4.
The Speedup Theorem Concluded
435
15
Polynomial-Time Computability
439
1.
Rates of Growth
439
2.
P
versus NP
443
3.
Cook s Theorem
451
4.
Other NP-Complete Problems
457
Contents xi
Part
5
Semantics
465
16
Approximation
Orderings
467
1.
Programming Language Semantics
467
2.
Partial Orders
472
3.
Complete Partial Orders
475
4.
Continuous Functions
486
5.
Fixed Points
494
17
Denotational Semantics of Recursion Equations
505
1.
Syntax
505
2.
Semantics of Terms
511
3.
Solutions to W-Programs
520
4.
Denotational Semantics of W-Programs
530
5.
Simple Data Structure Systems
539
6.
Infinitary Data Structure Systems
544
18
Operational Semantics of Recursion Equations
557
1.
Operational Semantics for Simple Data Structure Systems
557
2.
Computable Functions
575
3.
Operational Semantics for Infinitary Data Structure Systems
584
Suggestions for Further Reading
593
Notation Index
595
Index
599
ΜΛΚί
IN
ІУ
W
ÍS
received his doctorate
from Princeton in
1^50.
Davis *s book:
tind
U
risolveteti
Iity (1P58)
has been called one of the few real
classics in computer science.** He is best
known for his work in
automi
and for his contributions to the
solution of Hubert s tenth problem, for
which later he was awarded the Chauvenct
and Lester R.. Ford Prizes by the American
Mathematical Association. Davis has been
on the faculty of the
Courant
Institute, New
York: University, since 1<>65. He is
Professor of Mathematics and Computer
Science and has been Chair of the
Computer Science Department.
Kí
ł)
^* ѕи
,
м
was a systems programmer
before receiving his Ph.D. in Computer
Science from New York University in
1983.
Since then he has held positions at
the City University of New^ York, the
University of Catania in Italy, and Yale
University. His research interests include
computational complexity, logic
Ogramming, and programming language
Fl
ΛΙΝΗ
J. WHYl KľR
__________ _
în
Computer
Science
from Rutgers, the
State University of New
J
was in the
particularly softw
the secretary/treasurer of ACM/SIGSOFT
and is currently a member of the executive
committee of the IEEE/Computer Society
Technical Committee on Software
ring. She has been a charter
ж
of the Committee on the Status of
J*M*JV5iIíř Rceeilrcn
Association. She is
ofessor of Computer Science at
Institute. New York University,
This book is a rigorous but readable
introduction to some of the central topics in
theoretical computer science. The main
subjects are computabiiity theory, formal
languages, logic and automated deduction,
computational complexity (including
NP-completenessK and programming
language semantics.
Features of the second edition:
Computability theory is introduced in a
manner that makes maximum use of
previous programming experience,
including a universal program that
takes up less than a page.
The number of exercises included has
more than tripled.
Automata theory, computational logic,
and complexity theory are presented in
a flexible manner and can be covered in
a variety of different arrangements.
A new section on the denotational and
operational semantics of recursion
equations has been added.
|
any_adam_object | 1 |
author | Davis, Martin 1928-2023 Sigal, Ron Weyuker, Elaine J. |
author_GND | (DE-588)116040866 (DE-588)135877199 |
author_facet | Davis, Martin 1928-2023 Sigal, Ron Weyuker, Elaine J. |
author_role | aut aut aut |
author_sort | Davis, Martin 1928-2023 |
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bvnumber | BV009753726 |
classification_rvk | ST 136 |
classification_tum | DAT 500f |
ctrlnum | (OCoLC)246798387 (DE-599)BVBBV009753726 |
discipline | Informatik |
edition | 2. ed. |
format | Book |
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id | DE-604.BV009753726 |
illustrated | Illustrated |
indexdate | 2024-07-09T17:40:17Z |
institution | BVB |
isbn | 0122063821 |
language | English |
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physical | XIX, 609 S. graph. Darst. |
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spelling | Davis, Martin 1928-2023 Verfasser (DE-588)116040866 aut Computability, complexity, and languages fundamentals of theoretical computer science Martin D. Davis ; Ron Sigal ; Elaine J. Weyuker 2. ed. San Diego, Calif. [u.a.] Acad. Press 1994 XIX, 609 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computer science and scientific computing Hier auch später erschienene, unveränderte Nachdrucke Automatentheorie (DE-588)4003953-5 gnd rswk-swf Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf Komplexität (DE-588)4135369-9 gnd rswk-swf Berechenbarkeit (DE-588)4138368-0 gnd rswk-swf Formale Sprache (DE-588)4017848-1 gnd rswk-swf Automatentheorie (DE-588)4003953-5 s DE-604 Komplexität (DE-588)4135369-9 s Berechenbarkeit (DE-588)4138368-0 s Formale Sprache (DE-588)4017848-1 s Theoretische Informatik (DE-588)4196735-5 s Sigal, Ron Verfasser aut Weyuker, Elaine J. Verfasser (DE-588)135877199 aut Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006451035&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006451035&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
spellingShingle | Davis, Martin 1928-2023 Sigal, Ron Weyuker, Elaine J. Computability, complexity, and languages fundamentals of theoretical computer science Automatentheorie (DE-588)4003953-5 gnd Theoretische Informatik (DE-588)4196735-5 gnd Komplexität (DE-588)4135369-9 gnd Berechenbarkeit (DE-588)4138368-0 gnd Formale Sprache (DE-588)4017848-1 gnd |
subject_GND | (DE-588)4003953-5 (DE-588)4196735-5 (DE-588)4135369-9 (DE-588)4138368-0 (DE-588)4017848-1 |
title | Computability, complexity, and languages fundamentals of theoretical computer science |
title_auth | Computability, complexity, and languages fundamentals of theoretical computer science |
title_exact_search | Computability, complexity, and languages fundamentals of theoretical computer science |
title_full | Computability, complexity, and languages fundamentals of theoretical computer science Martin D. Davis ; Ron Sigal ; Elaine J. Weyuker |
title_fullStr | Computability, complexity, and languages fundamentals of theoretical computer science Martin D. Davis ; Ron Sigal ; Elaine J. Weyuker |
title_full_unstemmed | Computability, complexity, and languages fundamentals of theoretical computer science Martin D. Davis ; Ron Sigal ; Elaine J. Weyuker |
title_short | Computability, complexity, and languages |
title_sort | computability complexity and languages fundamentals of theoretical computer science |
title_sub | fundamentals of theoretical computer science |
topic | Automatentheorie (DE-588)4003953-5 gnd Theoretische Informatik (DE-588)4196735-5 gnd Komplexität (DE-588)4135369-9 gnd Berechenbarkeit (DE-588)4138368-0 gnd Formale Sprache (DE-588)4017848-1 gnd |
topic_facet | Automatentheorie Theoretische Informatik Komplexität Berechenbarkeit Formale Sprache |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006451035&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006451035&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT davismartin computabilitycomplexityandlanguagesfundamentalsoftheoreticalcomputerscience AT sigalron computabilitycomplexityandlanguagesfundamentalsoftheoreticalcomputerscience AT weyukerelainej computabilitycomplexityandlanguagesfundamentalsoftheoreticalcomputerscience |