Theoretical foundations of computer science:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Malabar, Fla.
Krieger
1993
|
| Edition: | Reprint ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXV, 478 S. graph. Darst. |
| ISBN: | 0894647989 |
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MARC
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| 245 | 1 | 0 | |a Theoretical foundations of computer science |c Dino Mandrioli ; Carlo Ghezzi |
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Record in the Search Index
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|---|---|
| adam_text | Theoretical
Foundations of
Computer Science
Dino IVtandrioli
Carlo Ghezzi
KRIEGER PUBLISHING COMPANY
MALABAR, FLORIDA
Contents
CHAPTER 0 MATHEMATICAL BACKGROUND
Mathematical Glossary
Basic]
Sets, Relations, Functions
Basic Algebraic Structures
Permutations and Combinations
Graphs and Trees
Alphabets, Strings, and Languages
Elements of Mathematical Logic
Introduction to Formal Theories
Propositional Calculus (^ ?)
First-Order Theories and Predicate
Calculi
A amp;$ for Arithmetic and Its Functions
0241 Peano s Axioms
0242 Recursive Functions
xiii
xiv Contents
024 3* Some Fundamental Properties of
the Axiomatization of Arithmetic 37
Chapter Summary 41
Bibliographic Remarks 41
CHAPTER 1 MODELS FOR COMPUTER SCIENCE:
AUTOMATA AND GRAMMARS 43
The Use of Models in Engineering and Science
111 Introductory Examples
112 What About Models for the Computer
Scientist?
Finite-State Automata
121 Finite-State Automata as Language
Acceptors
122 Finite-State Automata as Language
Translators
123 Properties of Finite-State Automata
Extending Finite-State Automata:
The Pushdown Automaton
131 Pushdown Automata as Language
Acceptors
132 Pushdown Automata as Language
Translators
133 Properties of Pushdown Automata
and Their Relation to
Finite-State Automata
Turing Machines
141 Turing Machines as Language
Acceptors
142 Turing Machines as Language
Translators
143 Turing Machines as Function
Evaluators
144 Properties of Turing Machines
Grammars: A Formalism to Generate Languages
151 Properties of Grammars
Denotational Language Definitions
161 Equations in Language Spaces
162 Regular Expressions
Contents X V
1 7 Nondeterministic Models 119
171 Nondeterministic Finite-State
Automata 120
172 Nondeterministic Pushdown Automata
and Nondeterministic Turing Machines 124
1 7 3* An Intrinsically Nondeterministic
Evolutionary Model: Petri Nets 127
1731 Petri Nets As Language
Recognizers 132
174 Some Remarks on Nondeterministic
Versus Stochastic Models 134
1 8 On the Power Relations Among Formalisms 135
Chapter Summary 138
Further Exercises 139
Sketchy Solutions to Selected Exercises 140
Appendix
LA The Equivalence Between Turing Machines
and Partial Recursive Functions 142
Bibliographic Remarks 145
CHAPTER 2 SOLVABLE AND UNSOLVABLE
PROBLEMS 147
2 1 On the Ability of a Mechanism to Solve
a Problem 147
2 2 On the Formalization of the Notion of
a Problem 148
2 3 Turing Machines, Programming Languages,
and Church s Thesis (Part 1) 151
2 4 Algorithms and Church s Thesis (Part 2) 152
2 5 Turing Machine Enumeration and Universal
Turing Machines 156
251 Turing Machine Enumeration 157
252 Universal Turing Machines 160
2 6 Unsolvable Problems 163
2 7 More on Solvable and Unsolvable Problems 166
2 8 Fundamental Statements of Computability
Theory 169
281 Recursive and Recursively
Enumerable Sets 169
282 Kleene s and Rice s Theorems 174
vyj • Contents
i
2 9 Reasoning on Problem Unsolvability 176
2 10 Solvable and Unsolvable Language Problems 179
2 11* Problem Reducibility and Degrees
of Unsolvability 182
Chapter Summary 187
Further Exercises 188
Sketchy Solutions to Selected Exercises 189
Bibliographic Remarks 190
CHAPTER 3 THE COMPLEXITY OF COMPUTING 193
3 1 Problem Solving in Practice: Some Difficulties 193
311 How to Define Complexity Precisely 197
312 Asymptotic Behavior 198
313 Other Sources of Complexity 200
3 2 Complexity Analysis by Means of Automata 201
321 The Complexity of Problem Solving
by Turing Machines 201
322 The Complexity of Problem Solving
by Other Automata 209
3221 Complexity of Finite-State
Automata Computations 209
3222 Complexity of Push-Down
Automata Computations 210
3223 Complexity of Single-Tape
Turing Machines 212
3 3 Some General Properties of Multitape
Turing Machines Complexity 218
3 4 Complexity Analysis of Real
Computer Programs 225
341 The RAM Machine 226
342 Higher-Level Programming Languages 237
3 5 Putting Things Together 244
3 6* Advanced Complexity Concepts: Hierarchies,
Reducibility, and Completeness 253
3 7* Some Classical /T^-Complete Problems 259
3 8 Complexity Lower Bounds 268
3 9 Complexity Evaluation in Action 272
391A Sorting Example 272
392 An Algorithm on Graphs 275
3 10 Some Advice and Conclusions 279
Contents XVM
»
Chapter Summary 281
Further Exercises 281
Sketchy Solutions to Selected Exercises 282
Bibliographic Remarks 283
CHAPTER 4 FORMAL SEMANTICS 285
4 1 Notation and Meaning 285
4 2 The Need for a Formal Definition of Semantics 290
4 3 The Use of Formal Semantics 292
4 4 Main Approaches to Giving Formal Semantics
of Programming Languages 294
441 The Operational Approach to
Semantics 295
442 The Denotational Approach to
Semantics 296
4 5 Operational Semantics 298
451 SMALG+: Syntax and Informal
Semantics 298
452 Description of SMALM+ 302
453 Semantics of SMALG+ Defined
via SMALM + 306
4 6 Denotational Semantics 315
461 McCarthy s Formalism and
Its Semantics 316
4611 Mathematical Background 329
4612 Denotational Semantics of
McCarthy s Formalism 339
462 McCarthy s Formalism as a
Programming Language 344
463 Denotational Semantics for
Algol-like Languages 347
4 7 Concluding Remarks 354
Chapter Summary 356
Further Exercises 356
Sketchy Solutions to Selected Exercises 357
Appendix
4 A Equivalence Between McCarthy s Formalism,
Partial Recursive Functions,
and Turing Machines 358
Bibliographic Remarks 359
xviii
CHAPTER 5 PROVING PROGRAM PROPERTIES 361
5 4*
5 5*
5 7*
The Impact of Formal Techniques on Program
Reliability
A Proof-Oriented Formal Semantics:
The Axiomatic Approach
521 Handling Quantified Assertions
522 Handling Indexed Variables
The Termination Issue
5 3 1* Further Insights into Termination
Proofs
The Soundness and Completeness Issues
The Synthesis of Correct Programs
Towards a Proof-System for a Real-Life
Programming Language
Proving Further Program Properties:
The Case of Complexity
5 7 1* Termination as Corollary of Complexity
Proving Program Properties Through
Denotational Semantics
Concluding Remarks
Chapter Summary 416
Further Exercises 416
Sketchy Solutions to Selected Exercises 417
Bibliographic Remarks 419
CHAPTER 6 NONDETERMINISM AND
PARALLEL COMPUTATION 421
6 1 Introduction 421
6 2 The Use of Nondeterminism and Parallelism in
Classical Programming 422
621 Nondeterministic Algorithms for
Search Problems 422
622 Parallel Computation: An Example 426
623 Nondeterministic Programming
Languages and Correctness
Proofs: A Brief Introduction 428
6 3 Concurrent Computations and the Use
of Nondeterministic Models 432
631 Petri Nets and the Description of
Operating Systems 440
xix
Describing Shared Databases by
Means of Petri Nets
Real-Time Systems and Petri Nets
Describing Semantics of
Concurrent Programming Languages:
Examples from Ada
Describing Distributed Systems by
Means of Petri Nets
Chapter Summary 455
Further Exercises 455
Sketchy Solutions to Selected Exercises 456
Bibliographic Remarks 457
BIBLIOGRAPHY 459
INDEX 471
|
| any_adam_object | 1 |
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| bvnumber | BV023807601 |
| classification_rvk | ST 130 |
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| discipline | Informatik |
| edition | Reprint ed. |
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| institution | BVB |
| isbn | 0894647989 |
| language | English |
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| physical | XXV, 478 S. graph. Darst. |
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| publisher | Krieger |
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| spelling | Mandrioli, Dino Verfasser aut Theoretical foundations of computer science Dino Mandrioli ; Carlo Ghezzi Reprint ed. Malabar, Fla. Krieger 1993 XXV, 478 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf Theoretische Informatik (DE-588)4196735-5 s DE-604 Mathematische Logik (DE-588)4037951-6 s Ghezzi, Carlo Verfasser aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017449771&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mandrioli, Dino Ghezzi, Carlo Theoretical foundations of computer science Mathematische Logik (DE-588)4037951-6 gnd Theoretische Informatik (DE-588)4196735-5 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4196735-5 |
| title | Theoretical foundations of computer science |
| title_auth | Theoretical foundations of computer science |
| title_exact_search | Theoretical foundations of computer science |
| title_full | Theoretical foundations of computer science Dino Mandrioli ; Carlo Ghezzi |
| title_fullStr | Theoretical foundations of computer science Dino Mandrioli ; Carlo Ghezzi |
| title_full_unstemmed | Theoretical foundations of computer science Dino Mandrioli ; Carlo Ghezzi |
| title_short | Theoretical foundations of computer science |
| title_sort | theoretical foundations of computer science |
| topic | Mathematische Logik (DE-588)4037951-6 gnd Theoretische Informatik (DE-588)4196735-5 gnd |
| topic_facet | Mathematische Logik Theoretische Informatik |
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