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Encyclopedia > On Computable Numbers

This is a list of important publications in computer science, organized by field.


Some reasons why a particular publication might be regarded as important:

  • Topic creator – A publication that created a new topic
  • Breakthrough – A publication that changed scientific knowledge significantly
  • Introduction – A publication that is a good introduction or survey of a topic
  • Influence – A publication which has significantly influenced the world
  • Latest and greatest – The current most advanced result in a topic
Contents

Computability

On computable numbers, with an application to the Entscheidungsproblem

Description: This article set the limits of computer science. It defined the Turing Machine, a model for all computations. On the other hand it proved the undecidability of the halting problem and Entscheidungsproblem and by doing so found the limits of possible computation.


Importance: Topic creator, Breakthrough, Influence


On certain formal properties of grammars

Description: The Chomsky hierarchy, a containment hierarchy of classes of formal grammars that generate formal languages was introduced.


Importance: Topic creator, Breakthrough, Influence


Finite automata and their decision problem

  • Michael O. Rabin and Dana S. Scott
  • IBM J. Research and Development, 3:114--125, 1959.
  • Online version (http://domino.research.ibm.com/tchjr/journalindex.nsf/0/cdf6b2949432156385256bfa00683d63?OpenDocument)

Description: Mathematical treatment of automata, proof of core properties, and definition of non-deterministic finite automaton


Importance: Topic creator, Breakthrough, Influence, Introduction


Computational complexity theory

On the computational complexity of algorithms

Description: This paper gave computational complexity its name and seed.


Importance: Topic creator, Breakthrough, Influence


The complexity of theorem proving procedures

  • S. A. Cook
  • Proceedings of the 3rd Annual ACM Symposium on Theory of Computing (1971), pp. 151--158.

Description: This paper introduced the concept of NP-Completeness and proved that Boolean satisfiability problem(SAT) is NP-Complete.


Importance: Topic creator, Breakthrough, Influence


Reducibility among combinatorial problems

  • R. M. Karp
  • In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pages 85-103. Plenum Press, New York, NY, 1972.

Description: This paper showed that 21 different problems are NP-Complete and showed the importance of the concept.


Importance: Influence


Computers and Intractability: A Guide to the Theory of NP-Completeness

Description: The main importance of this book is due to its extensive list of more than 300 NP-Complete problems. This list became a common reference and definition. It is important to note that though the book was published only few years after the concept was defined such an extensive list was found.


Importance: Introduction, Influence, Latest and greatest


Theory and Applications of Trapdoor functions

  • Andrew Chi-Chih Yao
  • Proc. 23rd Symposium on the Foundations of Computer Science (1982), pp. 80--91

Description: This paper introduced the concept of Trapdoor functions and described some of its application, like in cryptography.


Importance: Topic creator, Breakthrough


The Knowledge Complexity of Interactive Proof Systems

Description: This paper introduced the concept of zero knowledge.


Importance: Topic creator, Breakthrough


How to Construct Random Functions

Description: This paper showed that the existence of one way functions leads to computational randomness.


Importance: Topic creator, Breakthrough, Latest and greatest, Influence


IP = PSPACE

  • Adi Shamir
  • Journal of the ACM, 39(4):869-877, 1992.

Description: IP is a complexity class whose characterization is quite different from the usual time/space bounded computational classes. In this paper Shamir showed the IP = PSPACE, hence each problem in one complexity class is solvable in the other.


Importance: Breakthrough


Computational Complexity

  • C.H. Papadimitriou
  • Addison-Wesley, 1994. ISBN 0201530821

Description: This book provides a very good introduction to Computational Complexity


Importance: Introduction


Algorithms

A machine program for theorem proving

Description: The DLL algorithm. The basic algorithm for SAT and other NP-Complete problems.


Importance: Breakthrough, Influence


A Machine-Oriented Logic Based on the Resolution Principle

  • J. Alan Robinson
  • Comms. ACM, 5:23--41, 1965.

Description: First description of resolution and unification used in theorem proving; used in Prolog & logic programming.


Importance: Topic Creator, Breakthrough, Influence


Optimization by simulated annealing

  • Kirkpatrick, S., Gelatt, C., & Vecchi, M.
  • Science, Number 4598, 13,pages 671-680, May 1983.
  • Online copy (http://citeseer.ist.psu.edu/kirkpatrick83optimization.html)

Description: A very common heuristic for NP-Complete problems.


Importance: Influence


The Art of Computer Programming

Description: This set of textbooks used to be very popular algorithms books. The algorithms were written in the MIX assembly language. Due to that, the algorithms were very precise but not very readable...


Importance: Influence


Introduction to Algorithms

Description: As its name indicates this textbook is a very good introduction to algorithms. This book became so popular that it is almost the de facto standard for basic algorithms teaching.


Importance: Introduction, Influence


Algorithmic information theory

A formal theory of inductive inference

  • Ray Solomonoff
  • Inform. and Control, vol. 7, pp. 1--22, March 1964; pp. 224--254, June 1964.

Description: This was the beginning of Algorithmic information theory and Kolmogorov complexity. Note that though Kolmogorov complexity is named after Andrey Kolmogorov, he said that the seeds of that idea are due to Ray Solomonoff. Andrey Kolmogorov contributed a lot to this area but in later articles.


Importance: Topic creator, Breakthrough, Influence


Algorithmic information theory

  • Gregory Chaitin
  • IBM Journal of Research and Development 21 (1977), pp. 350-359, 496.
  • Online version (http://www.cs.auckland.ac.nz/CDMTCS/chaitin/ibm.pdf)

Description: A good introduction to Algorithmic information theory by one of the important people in the area.


Importance: Introduction


Information theory

A mathematical theory of communication

  • C.E. Shannon
  • Bell System Technical Journal, 27:379--423,623--656, 1948
  • Online copy (HTML) (http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html)

Description: This paper created communication theory and information theory.


Importance: Topic creator, Breakthrough, Introduction, Influence


Error detecting and error correcting codes

  • Richard Hamming
  • Bell Systems Technical Journal, vol. 29, pp. 147--160, 1950
  • Online copy (http://www.engelschall.com/~sb/hamming/?page=1)

Description: In this paper, Hamming introduced the idea of error-correcting code. He created the Hamming code and the Hamming distance and developed methods for code optimality proofs.


Importance: Topic creator, Breakthrough, Introduction, Influence


A Method for the Construction of Minimum Redundancy Codes

  • David A. Huffman
  • Proceedings of the Institute of Radio Engineers, September 1952, Volume 40, Number 9, pp. 1098-1101.

Description: The Huffman coding.


Importance: Influence, Breakthrough


A Universal Algorithm for Sequential Data Compression

  • Jacob Ziv
  • Abraham Lempel
  • IEEE Transactions on Information Theory, Vol. 23, No. 3, pp. 337-343.
  • Online copy (http://citeseer.nj.nec.com/ziv77universal.html)

Description: The LZ77 compression algorithm.


Importance: Influence, Breakthrough


Elements of Information Theory

  • T. M. Cover
  • J. A. Thomas
  • Wiley, 1991.

Description: A good and popular introduction to information theory.


Importance: Influence, Introduction


Operating system

An experimental timesharing system.

Description: This paper discuss timesharing as a method of sharing computer resource. This idea changed the interaction with computer systems.


Importance: Influence


The UNIX Time-Sharing System

  • Dennis M. Ritchie and Ken Thompson
  • Communications of ACM 7, 7, July 1974.
  • Online copy (few formats) (http://citeseer.ist.psu.edu/ritchie74unix.html)

Description: The Unix operating system and its principles were described in this paper. The main importance is not of the paper but of the operating system, which had tremendous effect on operating system and computer technology.


Importance: Influence, Breakthrough


Scheduling Techniques for Concurrent Systems

  • J. K. Ousterhout
  • Proceedings of Third International Conference on Distributed Computing Systems, 1982, 22—30.

Description: Algorithms for coscheduling of related processes were given


Importance: Influence


Databases

A relational model for large shared data bank

  • E. F. Codd
  • Communications of the ACM, 13(6):377-- 387, June 1970

Description: This paper introduced the relational model for databases. This model became the number one model.


Importance: Topic creator, Breakthrough, Influence


The Entity Relationship Model - Towards a Unified View of Data

  • P.P-S. Chen
  • ACM Transactions on Database Systems, Vol. 1, No. 1, March 1976, pp. 9-36

Description: This paper introduced the Entity-relationship diagram(ERD) method of database design.


Importance: Breakthrough, Influence


Mining association rules between sets of items in large databases

  • Rakesh Agrawal, Tomasz Imielinski, Arun Swami
  • Proc. of the ACM SIGMOD Conference on Management of Data, pages 207--216, Washington, D.C., May 1993
  • Online copy (HTML) (http://citeseer.nj.nec.com/agrawal93mining.html)

Description: Association rules, a very common method for data mining.


Importance: Topic creator, Introduction, Influence


Cryptography

Communication Theory of Secrecy Systems

  • C.E. Shannon
  • " Communication Theory of Secrecy Systems", Bell System Technical Journal, vol.28-4, page 656--715, 1949.
  • Online copy (PDF) (http://www.cs.ucla.edu/~jkong/research/security/shannon1949.pdf)

Description: Information theory based analysis of cryptography.


Importance: Breakthrough, Introduction, Influence


New directions in cryptography

  • W.Diffie, M.E.Hellman
  • IEEE Trans. Inform. Theory, IT-22, 6, 1976, pp.644-654
  • Online copy (HTML) (http://citeseer.nj.nec.com/340126.html)

Description: This paper suggested public key cryptography and presented Diffie-Hellman key exchange.


Importance: Topic creator, Breakthrough, Introduction, Influence, Latest and greatest (A great paper from every perspective...)


A Method for Obtaining Digital Signatures and Public Key Cryptosystems

  • R. Rivest, A. Shamir, L. Adleman
  • Communications of the ACM, Vol. 21 (2), 1978, pages 120--126
  • Online copy (HTML) (http://citeseer.nj.nec.com/rivest78method.html)

Description: The RSA encryption method. The first public key encryption method.


Importance: Breakthrough, Influence


How to Share a Secret

Description: A safe method for sharing a secret.


Importance: Topic creator, Breakthrough


Artificial intelligence

Computing machinery and intelligence

Description: This paper discusses whether machine can think and suggested the Turing test as a method for checking it. In a sense, this was the beginning of artificial intelligence


Importance: Topic creator, Breakthrough, Influence


A Proposal for the Dartmouth Summer Research Project on Artificial Intelligence

Description: This summer research proposal marks the areas of research in artificial intelligence since then. It was a very long summer.


Importance: Influence


Machine learning

Language identification in the limit

  • E. M. Gold
  • Information and Control, 10:447--474, 1967

Description: This paper created Algorithmic learning theory.


Importance: Topic creator, Breakthrough, Influence


On the uniform convergence of relative frequencies of events to their probabilities

Description: Computational learning theory, VC theory, statistical uniform convergence and the VC dimension.


Importance: Breakthrough, Influence


A theory of the learnable

  • Leslie Valiant
  • Communications of the ACM, 27(11): 1134--1142 (1984)

Description: The Probably approximately correct learning (PAC learning) framework.


Importance: Topic creator, Breakthrough, Influence


Learnability and the Vapnik-Chervonenkis dimension

  • A. Blumer
  • A. Ehrenfeucht
  • D. Haussler
  • M. K. Warmuth
  • Journal of the ACM, 36(4):929--965, 1989.

Description: The complete characterization of PAC learnability using the VC dimension.


Importance: Breakthrough, Influence


Cryptographic limitations on learning boolean formulae and finite automata

  • M. Kearns
  • L. G. Valiant
  • In Proceedings of the 21st Annual ACM Symposium on Theory of Computing, pages 433--444, New York. ACM.
  • Online version(HTML) (http://citeseer.ist.psu.edu/kearns89cryptographic.html)

Description: Proving negative results for PAC learning.


Importance: Influence


The strength of weak learnability

  • Robert E. Schapire
  • Machine Learning, 5(2):197--227, 1990.
  • Online version(HTML) (http://citeseer.nj.nec.com/schapire90strength.html)

Description: Proving that weak and strong learnability are equivalent in the noise free PAC framework.


Importance: Breakthrough, Influence


Learning in the presence of malicious errors

  • Michael Kearns
  • Ming Li
  • Journal on Computing, 22(4):807--837, August 1993.
  • Online version(HTML) (http://citeseer.nj.nec.com/kearns93learning.html)

Description: Proving possibility and imposibility result in the malicious errors framework.


Importance: Breakthrough, Influence


Computer vision

The Phase Correlation Image Alignment Method

  • C.D. Kuglin and D.C. Hines
  • IEEE 1975 Conference on Cybernetics and Society, 1975, New York, p. 163--165, September

Description: A correlation method based upon the inverse Fourier transform


Importance: Influence


An Iterative Image Registration Technique with an Application to Stereo Vision

  • Lucas, B.D. and Kanade, T.
  • Proceedings of the 7th International Joint Conference on Artificial Intelligence, 674--679,Vancouver, Canada,1981
  • Online version (http://citeseer.ist.psu.edu/lucas81iterative.html)

Description: This paper provides efficient technique for image registration


Importance: Influence


The Laplacian Pyramid as a compact image code

  • Peter J. Burt and Edward H. Adelson
  • IEEE Transactions on Communications, volume = "COM-31,4", p. 532--540,1983.
  • Online version (http://citeseer.ist.psu.edu/burt83laplacian.html)

Description: A technique for image encoding using local operators of many scales


Importance: Influence


Condensation -- conditional density propagation for visual tracking

  • M. Isard and A. Blake
  • International Journal of Computer Vision 29(1), pp. 5--28, 1998.
  • Online version (http://citeseer.ist.psu.edu/isard98condensation.html)

Description: A technique for visual tracking


Importance: Influence


Compilers

YACC: Yet another compiler-compiler

  • Stephen C. Johnson
  • Unix Programmer's Manual Vol 2b, 1979
  • Online copy (HTML) (http://citeseer.nj.nec.com/johnson79yacc.html)

Description: Yacc is a tool that made compiler writing much easier.


Importance: Influence


Compilers: Principles, Techniques and Tools

Description: This book became a classic in compiler writing. It is also known as the Dragon book, after the (red) dragon that appears on its cover.


Importance: Introduction, Influence


Formal verification

Assigning meanings to programs

  • Robert W. Floyd
  • Mathematical Aspects of Computer Science, pages 19-32, 1967

Description: Introduced the idea of attaching logical assertions to points in a program in order to prove its correctness and influenced C. A. R. Hoare's seminal work on program verification.


Importance: Topic creator, Breakthrough, Influence, Introduction


An axiomatic basis for computer programming

Description: Axiomatic foundation for program correctness proofs was laid. The importance of the use of formal methods is explained.


Importance: Topic creator, Breakthrough, Influence, Introduction


The temporal logic of programs

  • Amir Pnueli
  • In Proc. 18th IEEE Symposium on Foundation of Computer Science, pages 46--57, 1977.

Description: The use of temporal logic was suggested as a method for formal verification. Importance: Topic creator, Influence


Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints

  • Patrick and Radhia Cousot
  • In Proc. 4th ACM Symposium on Principles of Programming Languages, 238--252, 1977

Description: Introducing abstract interpretation for the verification of computer programs by sound approximations.


Importance: Topic creator, Influence.


Model Checking

Description: An overview of Model checking, an automatic formal verification technique Importance: Introduction


Software engineering

Go To Statement Considered Harmful

  • Dijkstra, E. W.
  • Communications of the ACM, 11(3), 147-148, March 1968
  • Online copy (HTML) (http://www.acm.org/classics/oct95/)

Description: Don't use goto - the beginning of structured programming.


Importance: Topic creator, Influence


On the criteria to be used in decomposing systems into modules

  • David Parnas
  • Communications of the ACM, December:1053-1058, December 1972.
  • Online copy (HTML) (http://www.acm.org/classics/may96/)

Description: The importance of modularization and information hiding.


Importance: Influence


The Mythical Man-Month: Essays on Software Engineering

Description: Throwing more people at the task will not speed its completion...


Importance: Influence


No Silver Bullet: Essence and Accidents of Software Engineering

Description: We will keep having problems with software...


Importance: Influence


The Cathedral and the Bazaar

Description: Open source methodology.


Importance: Influence


Design Patterns: Elements of Reusable Object Oriented Software

Description: This book was the first to define and list design patterns in computer science


Importance: Topic creator, Influence


Parallel computing

The Structure of "THE"-Multiprogramming System

  • Dijkstra, E. W.
  • Communication of the ACM, Vol. 11, No. 5 May 1968, pp. 345-346
  • Online copy (HTML) (http://www.acm.org/classics/mar96/)

Description: The introduction of basic primitives like mutex as the basis of multiprocessing programming.


Importance: Breakthrough, Influence


How to Make a Multiprocessor Computer That Correctly Executes Multiprocess Programs

  • Leslie Lamport
  • IEEE Transactions on Computers, volume C-28, number 9, p. 690-691, September, 1979.

Description: Requirements that guarantee the correct execution of multi process programs were defined.


Importance: Breakthrough, Influence


LogP: Towards a realistic model of parallel computation

  • D. Culler, R. Karp, D. Patterson, A. Sahay, K. E. Schauser, E. Santos, R. Subramonian, and T. von Eicken
  • In Proceedings 4th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, May 1993.
  • Online version (http://citeseer.nj.nec.com/culler93logp.html

  Results from FactBites:
 
Computable number - Wikipedia, the free encyclopedia (1350 words)
In mathematics, theoretical computer science and mathematical logic, the computable numbers, also known as the recursive numbers, are the subset of the real numbers consisting of the numbers which can be computed by a finite, terminating algorithm.
The computable numbers form a real closed field and can be used in the place of real numbers for many, but by no means all, mathematical purposes.
There are however many real numbers which are not computable: the set of all computable numbers is countable (because the set of algorithms is) while the set of real numbers is not (see Cantor's diagonal argument).
Wikipedia:WikiProject Numbers - Wikipedia, the free encyclopedia (3828 words)
It is a prime number, a Mersenne prime, a Fermat prime, a permutable prime, a palindromic prime, a composite number, a highly composite number, an abundant number, a surreal number, and an amicable number with 0.
It is the Xth prime number, the previous being Number N - 2x, with which it comprises a twin prime, the next being [[Number N + 2x]], with which it comprises a twin prime.
User:Egil's proposal for naming the articles Number N (number), and making the spelled out names of the numbers be redirects, (e.g, Four hundred and ninety-six redirects to 496 (number)), received the most votes, and with the initiative of User:Dysprosia, the articles were moved accordingly.
  More results at FactBites »


 

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