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This is a list of important publications in theoretical 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
 * Influence – A publication that has significantly influenced the world or has had a massive impact on the teaching of theoretical computer science.

On computable numbers, with an application to the Entscheidungsproblem

 * Alan Turing (1937)
 * Proceedings of the London Mathematical Society, Series 2, vol. 42, pp. 230–265, 1937, . Errata appeared in vol. 43, pp. 544–546, 1938,.
 * HTML version, PDF version

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.

Rekursive Funktionen
The first textbook on the theory of recursive functions. The book went through many editions and earned Péter the Kossuth Prize from the Hungarian government. Reviews by Raphael M. Robinson and Stephen Kleene praised the book for providing an effective elementary introduction for students.

Representation of Events in Nerve Nets and Finite Automata
Description: this paper introduced finite automata, regular expressions, and regular languages, and established their connection.
 * S. C. Kleene (1951)
 * U. S. Air Force Project Rand Research Memorandum RM-704, 1951
 * Online version
 * republished in:

Finite automata and their decision problems

 * Michael O. Rabin and Dana S. Scott (1959)
 * IBM Journal of Research and Development, vol. 3, pp. 114–125, 1959
 * Online version

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

On certain formal properties of grammars


Description: This article introduced what is now known as the Chomsky hierarchy, a containment hierarchy of classes of formal grammars that generate formal languages.

Decidability of second order theories and automata on infinite trees

 * Michael O. Rabin (1969)
 * Transactions of the American Mathematical Society, vol. 141, pp. 1–35, 1969

Description: The paper presented the tree automaton, an extension of the automata. The tree automaton had numerous applications to proofs of correctness of programs.

Cutland's Computability: An Introduction to Recursive Function Theory (Cambridge)


The review of this early text by Carl Smith of Purdue University (in the Society for Industrial and Applied Mathematics Reviews), reports that this a text with an "appropriate blend of intuition and rigor… in the exposition of proofs" that presents "the fundamental results of classical recursion theory [RT]... in a style... accessible to undergraduates with minimal mathematical background". While he states that it "would make an excellent introductory text for an introductory course in [RT] for mathematics students", he suggests that an "instructor must be prepared to substantially augment the material… " when it is used with computer science students (given a dearth of material on RT applications to this area).

Introduction to Automata Theory, Languages, and Computation

 * John E. Hopcroft, Jeffrey D. Ullman, and Rajeev Motwani (2001)
 * Addison-Wesley, 2001, ISBN 0-201-02988-X

Description: A popular textbook.

A letter from Gödel to von Neumann

 * Kurt Gödel (1956)
 * A Letter from Gödel to John von Neumann, March 20, 1956
 * Online version

Description: Gödel discusses the idea of efficient universal theorem prover.

Degree of difficulty of computing a function and a partial ordering of recursive sets


Description: This technical report was the first publication talking about what later was renamed computational complexity

The Intrinsic Computational Difficulty of Functions


Description: First definition of the complexity class P. One of the founding papers of complexity theory.

On the computational complexity of algorithms


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

A machine-independent theory of the complexity of recursive functions


Description: The Blum axioms.

How good is the simplex method?

 * Victor Klee and George J. Minty (1969)

Description: Constructed the "Klee–Minty cube" in dimension D, whose 2D corners are each visited by Dantzig's simplex algorithm for linear optimization.

The complexity of theorem proving procedures


Description: This paper introduced the concept of NP-Completeness and proved that Boolean satisfiability problem (SAT) is NP-Complete. Note that similar ideas were developed independently slightly later by Leonid Levin at "Levin, Universal Search Problems. Problemy Peredachi Informatsii 9(3):265–266, 1973".

Reducibility among combinatorial problems

 * R. M. Karp (1972)
 * In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, Plenum Press, New York, NY, 1972, pp. 85–103

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

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. Though the book was published only few years after the concept was defined such an extensive list was found.

How to construct random functions


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

The Knowledge Complexity of Interactive Proof Systems


Description: This paper introduced the concept of zero knowledge.

Algebraic methods for interactive proof systems


Description: This paper showed that PH is contained in IP.

IP = PSPACE


Description: IP is a complexity class whose characterization (based on interactive proof systems) is quite different from the usual time/space bounded computational classes. In this paper, Shamir extended the technique of the previous paper by Lund, et al., to show that PSPACE is contained in IP, and hence IP = PSPACE, so that each problem in one complexity class is solvable in the other.

Arora & Barak's Computational Complexity and Goldreich's Computational Complexity (both Cambridge)
Besides the estimable press bringing these recent texts forward, they are very positively reviewed in ACM's SIGACT News by Daniel Apon of the University of Arkansas, who identifies them as "textbooks for a course in complexity theory, aimed at early graduate… or... advanced undergraduate students… [with] numerous, unique strengths and very few weaknesses," and states that both are: The reviewer notes that there is "a definite attempt in [Arora and Barak] to include very up-to-date material, while Goldreich focuses more on developing a contextual and historical foundation for each concept presented," and that he "applaud[s] all… authors for their outstanding contributions."
 * Sanjeev Arora and Boaz Barak (2009) "Computational Complexity: A Modern Approach," Cambridge University Press, 579 pages, Hardcover
 * Oded Goldreich (2008) "Computational Complexity: A Conceptual Perspective, Cambridge University Press, 606 pages, Hardcover

Paths, trees, and flowers


Description: There is a polynomial time algorithm to find a maximum matching in a graph that is not bipartite and another step toward the idea of computational complexity. For more information see.

Theory and applications of trapdoor functions


Description: This paper creates a theoretical framework for trapdoor functions and described some of their applications, like in cryptography. Note that the concept of trapdoor functions was brought at "New directions in cryptography" six years earlier (See section V "Problem Interrelationships and Trap Doors.").

Computational Complexity

 * C.H. Papadimitriou
 * Addison-Wesley, 1994, ISBN 0-201-53082-1

Description: An introduction to computational complexity theory, the book explains its author's characterization of P-SPACE and other results.

Proof verification and the hardness of approximation problems


Description: These three papers established the surprising fact that certain problems in NP remain hard even when only an approximative solution is required. See PCP theorem.

"A machine program for theorem proving"


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

"A machine-oriented logic based on the resolution principle"


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

"The traveling-salesman problem and minimum spanning trees"


Description: The use of an algorithm for minimum spanning tree as an approximation algorithm for the NP-Complete travelling salesman problem. Approximation algorithms became a common method for coping with NP-Complete problems.

"A polynomial algorithm in linear programming"

 * L. G. Khachiyan (1979)
 * Soviet Mathematics - Doklady, vol. 20, pp. 191–194, 1979

Description: For long, there was no provably polynomial time algorithm for the linear programming problem. Khachiyan was the first to provide an algorithm that was polynomial (and not just was fast enough most of the time as previous algorithms). Later, Narendra Karmarkar presented a faster algorithm at: Narendra Karmarkar, "A new polynomial time algorithm for linear programming", Combinatorica, vol 4, no. 4, p. 373–395, 1984.

"Probabilistic algorithm for testing primality"


Description: The paper presented the Miller–Rabin primality test and outlined the program of randomized algorithms.

"Optimization by simulated annealing"


Description: This article described simulated annealing, which is now a very common heuristic for NP-Complete problems.

The Art of Computer Programming

 * Donald Knuth

Description: This monograph has four volumes covering popular algorithms. The algorithms are written in both English and MIX assembly language (or MMIX assembly language in more recent fascicles). This makes algorithms both understandable and precise. However, the use of a low-level programming language frustrates some programmers more familiar with modern structured programming languages.

Algorithms + Data Structures = Programs

 * Niklaus Wirth
 * Prentice Hall, 1976, ISBN 0-13-022418-9

Description: An early, influential book on algorithms and data structures, with implementations in Pascal.

The Design and Analysis of Computer Algorithms

 * Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman
 * Addison-Wesley, 1974, ISBN 0-201-00029-6

Description: One of the standard texts on algorithms for the period of approximately 1975–1985.

How to Solve It By Computer


Description: Explains the Whys of algorithms and data-structures. Explains the Creative Process, the Line of Reasoning, the Design Factors behind innovative solutions.

Algorithms

 * Robert Sedgewick
 * Addison-Wesley, 1983, ISBN 0-201-06672-6

Description: A very popular text on algorithms in the late 1980s. It was more accessible and readable (but more elementary) than Aho, Hopcroft, and Ullman. There are more recent editions.

Introduction to Algorithms

 * Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein
 * 3rd Edition, MIT Press, 2009, ISBN 978-0-262-03384-8.

Description: This textbook has become so popular that it is almost the de facto standard for teaching basic algorithms. The 1st edition (with first three authors) was published in 1990, the 2nd edition in 2001, and the 3rd in 2009.

"On Tables of Random Numbers"


Description: Proposed a computational and combinatorial approach to probability.

"A formal theory of inductive inference"

 * Ray Solomonoff
 * Information and Control, vol. 7, pp. 1–22 and 224–254, 1964
 * Online copy: part I, part II

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.

"Algorithmic information theory"


Description: An introduction to algorithmic information theory by one of the important people in the area.

"A mathematical theory of communication"


Description: This paper created the field of information theory.

"Error detecting and error correcting codes"


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.

"A method for the construction of minimum redundancy codes"


Description: The Huffman coding.

"A universal algorithm for sequential data compression"


Description: The LZ77 compression algorithm.

Elements of Information Theory


Description: A popular introduction to information theory.

Assigning meaning to programs


Description: Floyd's landmark paper introduces the method of inductive assertions and describes how a program (presented as a flow chart) annotated with first-order assertions may be shown to satisfy a pre- and post-condition specification. The paper also introduces the concepts of loop invariant and verification condition.

An axiomatic basis for computer programming


Description: Hoare's paper gives a set of logical rules for reasoning rigorously about the correctness of computer programs. It defines an Algol-like programming language using what are now called Hoare triples. It has been used as the basis for most later work in the field, rather than Floyd's paper "Assigning meaning to programs", which did the same in terms of flow charts.

Guarded Commands, Nondeterminacy and Formal Derivation of Programs


Description: Dijkstra's paper proposes (for the first time) that, instead of formally verifying a program after it has been written (i.e. post facto), programs and their formal proofs should be developed hand-in-hand (using predicate transformers to progressively refine weakest pre-conditions), a method known as program (or formal) refinement (or derivation), or sometimes "correctness-by-construction".

Proving Assertions about Parallel Programs

 * Ashcroft, Edward A. (1975) J. Comput. Syst. Sci. 10(1): 110–135

Description: The paper introduced invariance proofs of concurrent programs. It did not receive much attention because it discussed programs in terms of flow charts and was not written clearly enough.

An Axiomatic Proof Technique for Parallel Programs I


Description: This paper, along with the same authors' paper extends the axiomatic approach to parallel-program verification with the notion of Interference freedom.

A Discipline of Programming

 * Dijkstra, Edsger W. (1976)

Description: Dijkstra's classic postgraduate-level textbook extends his earlier paper Guarded commands, nondeterminacy and formal derivation of programs and firmly establishes the principle of formally deriving programs and their proofs hand-in-hand from their specifications.

The Temporal Logic of Programs
Description: Pnueli suggests temporal logic for formal verification in which the basic concept is the time dependence of events.

Communicating Sequential Processes


Description: Hoare's paper introduces the idea of concurrent processes (i.e. programs) that do not share variables but instead cooperate solely by exchanging synchronous messages. This has spurred great deal of research and advances, which are detailed in communicating sequential processes

Characterizing correctness properties of parallel programs using fixpoints
Description: Introduces model checking as a procedure to check correctness of concurrent programs.

A Calculus of Communicating Systems
Description: Milner's book describes a process algebra, called CCS, that permits systems of concurrent processes to be reasoned about formally, something that has not been possible for earlier models of concurrency (semaphores, critical sections, original CSP).

Software Development: A Rigorous Approach
Description: Jones' book is the first full-length exposition of the Vienna Development Method (VDM), which had evolved (principally) at IBM's Vienna research lab over the previous decade and which combines the idea of program refinement as per Dijkstra with that of data refinement (or reification) whereby algebraically defined abstract data types are formally transformed into progressively more "concrete" representations.

The Science of Programming


Description: This textbook describes Dijkstra's weakest precondition method of formal program derivation, except in a very much more accessible manner than Dijkstra's earlier A Discipline of Programming. It has jokingly been called "Dijkstra for the masses". The emphasis is on developing program and proof hand-in-hand, with the proof ideas leading the way. The examples in the book are small-scale, emphasizing basic algorithms, such as sorting, merging, and string manipulation. Subroutines (functions) are included, but not object-oriented and functional programming environments.

Denotational Semantics

 * Stoy, Joe (1981)

Description: This book is the first postgraduate-level book-length exposition of the mathematical (or functional) approach to the formal semantics of programming languages (in contrast to the operational and algebraic approaches).

Communicating Sequential Processes
Hoare, Tony (1985). Communicating Sequential Processes. Prentice Hall International Series in Computer Science. ISBN 978-0131532717 (hardback) or ISBN 978-0131532892 (paperback). (PDF available at http://www.usingcsp.com/)

Description: Hoare's book (currently the third most cited computer science reference of all time) presents an updated CSP model in which cooperating processes do not even have program variables and which, like CCS, permits systems of processes to be reasoned about formally.

Linear logic


Description: Girard's linear logic was a breakthrough in designing typing systems for sequential and concurrent computation, especially for resource conscious typing systems.

A Calculus of Mobile Processes
Description: This paper introduces the Pi-Calculus, a generalisation of CCS that allows process mobility. This extremely simple calculus has become the dominant paradigm in the theoretical study of programming languages, typing systems, and program logics. A second paper, which completes the work, can be downloaded here

Communication and Concurrency
Description: Milner's text is a more accessible, although still technically advanced, exposition of his earlier CCS work.

The Z Notation: A Reference Manual


Description: Spivey's classic text summarises the formal specification language Z notation, which, although originated by Jean-Raymond Abrial, had evolved (principally) at Oxford University over the previous decade.

a Practical Theory of Programming
Description: the up-to-date version of Predicative programming. The basis for C.A.R. Hoare's UTP. The simplest and most comprehensive formal methods. The latest online edition can be downloaded here