Professor Stephen A. Cook is a pioneer of the theory of computational complexity. His work on NP-completeness and the P vs. NP problem remains a central focus of this field. Cook won the 1982 Turing Award for "his advancement of our understanding of the complexity of computation in a significant and profound way." This volume includes a selection of seminal papers embodying the work that led to this award, exemplifying Cook's synthesis of ideas and techniques from logic and the theory of computation including NP-completeness, proof complexity, bounded arithmetic, and parallel and space-bounded computation. These papers are accompanied by contributed articles by leading researchers in these areas, which convey to a general reader the importance of Cook's ideas and their enduring impact on the research community. The book also contains biographical material, Cook's Turing Award lecture, and an interview. Together these provide a portrait of Cook as a recognized leader and innovator in mathematics and computer science, as well as a gentle mentor and colleague.
Author(s): Bruce M. Kapron, editor
Publisher: Association for Computing Machinery
Year: 2023
Language: English
Pages: 426
Cover
Halftitle
Title Page
Copyright Page
Contents
Introduction
Acknowledgments
PART I BIOGRAPHICAL BACKGROUND
Chapter 1 Stephen Cook: Complexity’s Humble Hero
1.1 Growing Up: Buffalo and Cows
1.2 The Lure of Mathematics
1.3 From Smooth Sailing to Rough Waters
1.4 Growing Roots, Making Waves
1.5 The Quiet Influencer
1.6 Profound and Complex
Chapter 2 ACM Interview of Stephen A. Cook by Bruce M. Kapron
PART II THE TURING AWARD LECTURE
Chapter 3 The 1982 ACM Turing Award Lecture
An Overview of Computational Complexity
Abstract
1 Early Papers
2 Early Issues and Concepts
3 Upper Bounds on Time
4 Lower Bounds
5 Probabilistic Algorithms
6 Synchronous Parallel Computation
7 The Future
Acknowledgments
References
PART III PERSPECTIVES ON COOK’S WORK
Chapter 4 Cook’s NP-completeness Paper and the Dawn of the New Theory
4.1 History
4.2 Cook’s Other 1971 Paper
4.3 The Paper at the 3rd STOC
4.4 The Mystery of Section 4.3
4.5 Aftermath
Chapter 5 The Cook–Reckhow Definition
5.1 Definition of Proof Systems
5.2 Simulations among Proof Systems
5.3 Hard Tautologies and the PHPn Formula
Acknowledgments
Chapter 6 Polynomially Verifiable Arithmetic
6.1 Introduction
6.2 The Equational Theory PV for Polynomial Time Computability
6.3 Extended Resolution and PV
6.4 Subsequent Developments
Acknowledgments
Chapter 7 Towards a Complexity Theory of Parallel Computation
7.1 First Words
7.2 The Early Years
7.3 The Beginnings of a Theory
7.4 Development and Issues with the Theory
7.5 Steve’s Class and Nick’s Class
7.6 Cook’s Surveys of Parallel Computation
7.7 Last Words
Chapter 8 Computation with Limited Space
8.1 Time and Space Bounds
8.2 Pebbling
8.3 Circuits
8.4 Branching Programs
PART IV SELECTED PAPERS
Chapter 9 The Complexity of Theorem-Proving Procedures
Summary
1 Tautologies and Polynomial Re-Reducibility
2 Discussion
3 The Predicate Calculus
4 More Discussion
References
Chapter 10 Characterizations of Pushdown Machines in Terms of Time-Bounded Computers
Abstract
Key words and Phrases
CR Categories
1 Introduction
2 Time-Bounded Computers
3 Other Machine Models
4 The Main Theorem
5 Applications of the Main Theorem
6 Conclusion and Open Questions
Acknowledgment
References
Chapter 11 The Relative Efficiency of Propositional Proof Systems
1 Introduction
2 Frege Systems
3 Natural Deduction Systems
4 Extended Frege Systems
5 The Substitution Rule
References
Chapter 12 Feasibly Constructive Proofs and the Propositional Calculus (Preliminary Version)
1 Introduction
2 The System PV
Rules of PV
3 The System PV1
4 The Gödel Incompleteness Theorem for PV
5 Propositional Calculus and the Main Theorem
6 Propositional Formulas Assigned to Equations of PV
7 PV as a Propositional Proof System
8 Conclusions and Future Research
Acknowledgments
References
Chapter 13 Towards a Complexity Theory of Synchronous Parallel Computation
Abstract
1 Introduction
2 Circuits and Alternating Turing Machines
3 Log Depth vs Log Space
4 Conglomerates and Aggregates
5 Hardware Modification Machines
6 Other Modifiable Models
7 Simultaneous Resource Bounds
8 Open Questions
Acknowledgment
References
Chapter 14 A Time-Space Tradeoff for Sorting on a General Sequential Model of Computation
Abstract
Key words
1 Introduction
2 The Formal Model and an Outline of the Proof
3 The Proof of the Main Lemma
4 Proof of the Main Theorem
5 Conclusion
Acknowledgment
References
Chapter 15 Pebbles and Branching Programs for Tree Evaluation
1 Introduction
2 Preliminaries
3 Connecting TMS, BPS, and Pebbling
4 Pebbling Bounds
5 Branching Program Bounds
6 Conclusion
Acknowledgments
References
PART V THE BERKELEY NOTES
Chapter 16 Cook’s Berkeley Notes
Chapter 17 A Survey of Classes of Primitive Recursive Functions
1 Basic Notions
2 The Grzegorczyk Hierarchy
3 Computation Time and Limited Recursion on Notation
4 The Ritchie Hierarchy
5 Other Classes
6 Summary of Facts and Open Questions
References
Chapter 18 Further Reading
Bibliography
Bibliography of the Works of Stephen A. Cook
References
Contributors’ Biographies
Index
