Theoretical computer science

Source: Wikipedia, the free encyclopedia.
This article is about the branch of computer science and mathematics. For the journal, see Theoretical Computer Science (journal).

Theoretical computer science (TCS) is a subset of general

formal language theory, the lambda calculus and type theory
.

It is difficult to circumscribe the theoretical areas precisely. The ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description:[1]

TCS covers a wide variety of topics including

rigor
.

History

Main article: History of computer science

While logical inference and mathematical proof had existed previously, in 1931

incompleteness theorem
that there are fundamental limitations on what statements could be proved or disproved.

NP-complete – a landmark result in computational complexity theory.[2]

Modern theoretical computer science research is based on these basic developments, but includes many other mathematical and interdisciplinary problems that have been posed, as shown below:

P = NP ?
Mathematical logic Automata theory Number theory Graph theory Computability theory Computational complexity theory
GNITIRW-TERCES
Cryptography Type theory Category theory Computational geometry Combinatorial optimization
Quantum computing theory

Topics

Algorithms

Main article: Algorithm

An algorithm is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning.

An algorithm is an

randomized algorithms, incorporate random input.[9]

Automata theory

Main article: Automata theory

Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science, under discrete mathematics (a section of mathematics and also of computer science). Automata comes from the Greek word αὐτόματα meaning "self-acting".

Automata Theory is the study of self-operating virtual machines to help in the logical understanding of input and output process, without or with intermediate stage(s) of computation (or any function/process).

Coding theory

Main article: Coding theory

data transmission
methods. This typically involves the removal of redundancy and the correction (or detection) of errors in the transmitted data.

Computational biology

Main article: Computational biology

Computational biology involves the development and application of data-analytical and theoretical methods, mathematical modeling and computational simulation techniques to the study of biological, behavioral, and social systems.[10] The field is broadly defined and includes foundations in computer science, applied mathematics, animation, statistics, biochemistry, chemistry, biophysics, molecular biology, genetics, genomics, ecology, evolution, anatomy, neuroscience, and visualization.[11]

Computational biology is different from

bioengineering and biology to build computers, but is similar to bioinformatics
, which is an interdisciplinary science using computers to store and process biological data.

Computational complexity theory

Main article: Computational complexity theory

computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm
.

A problem is regarded as inherently difficult if its solution requires significant resources, whatever the

models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage. Other complexity measures are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computational complexity theory is to determine the practical limits on what computers
can and cannot do.

Computational geometry

Main article: Computational geometry

Computational geometry is a branch of computer science devoted to the study of algorithms that can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry.

The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing (CAD/CAM), but many problems in computational geometry are classical in nature, and may come from mathematical visualization.

Other important applications of computational geometry include robotics (motion planning and visibility problems), geographic information systems (GIS) (geometrical location and search, route planning), integrated circuit design (IC geometry design and verification), computer-aided engineering (CAE) (mesh generation), computer vision (3D reconstruction).

Computational learning theory

Main article: Computational learning theory

Theoretical results in machine learning mainly deal with a type of inductive learning called supervised learning. In supervised learning, an algorithm is given samples that are labeled in some useful way. For example, the samples might be descriptions of mushrooms, and the labels could be whether or not the mushrooms are edible. The algorithm takes these previously labeled samples and uses them to induce a classifier. This classifier is a function that assigns labels to samples including the samples that have never been previously seen by the algorithm. The goal of the supervised learning algorithm is to optimize some measure of performance such as minimizing the number of mistakes made on new samples.

Computational number theory

Main article: Computational number theory

Computational number theory, also known as algorithmic number theory, is the study of algorithms for performing number theoretic computations. The best known problem in the field is integer factorization.

Cryptography

Main article: Cryptography

electronic commerce
.

Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed around

information-theoretically secure schemes that provably cannot be broken even with unlimited computing power—an example is the one-time pad
—but these schemes are more difficult to implement than the best theoretically breakable but computationally secure mechanisms.

Data structures

Main article: Data structure

A

data in a computer so that it can be used efficiently.[15][16]

Different kinds of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, databases use B-tree indexes for small percentages of data retrieval and compilers and databases use dynamic hash tables as look up tables.

Data structures provide a means to manage large amounts of data efficiently for uses such as large

secondary memory
.

Distributed computation

Main article:
Distributed computation

Distributed computing studies distributed systems. A distributed system is a software system in which components located on networked computers communicate and coordinate their actions by passing messages.[17] The components interact with each other in order to achieve a common goal. Three significant characteristics of distributed systems are: concurrency of components, lack of a global clock, and independent failure of components.[17] Examples of distributed systems vary from SOA-based systems to massively multiplayer online games to peer-to-peer applications, and blockchain networks like Bitcoin.

A computer program that runs in a distributed system is called a distributed program, and distributed programming is the process of writing such programs.[18] There are many alternatives for the message passing mechanism, including RPC-like connectors and message queues. An important goal and challenge of distributed systems is location transparency.

Information-based complexity

Main article: Information-based complexity

Information-based complexity (IBC) studies optimal algorithms and computational complexity for continuous problems. IBC has studied continuous problems as path integration, partial differential equations, systems of ordinary differential equations, nonlinear equations, integral equations, fixed points, and very-high-dimensional integration.

Formal methods

Main article: Formal methods

Formal methods are a particular kind of mathematics based techniques for the specification, development and verification of software and hardware systems.[19] The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design.[20]

Formal methods are best described as the application of a fairly broad variety of theoretical computer science fundamentals, in particular

algebraic data types to problems in software and hardware specification and verification.[21]

Information theory

Main article: Information theory

neurobiology,[22] the evolution[23] and function[24] of molecular codes, model selection in statistics,[25] thermal physics,[26] quantum computing, linguistics, plagiarism detection,[27] pattern recognition, anomaly detection and other forms of data analysis.[28]

Applications of fundamental topics of information theory include

algorithmic complexity theory, algorithmic information theory, information-theoretic security
, and measures of information.

Machine learning

Main article: Machine learning

scientific discipline that deals with the construction and study of algorithms that can learn from data.[29] Such algorithms operate by building a model based on inputs[30]
: 2  and using that to make predictions or decisions, rather than following only explicitly programmed instructions.

Machine learning can be considered a subfield of computer science and

spam filtering, optical character recognition (OCR),[31] search engines and computer vision. Machine learning is sometimes conflated with data mining,[32] although that focuses more on exploratory data analysis.[33] Machine learning and pattern recognition
"can be viewed as two facets of the same field."[30]: vii 

Parallel computation

Main article:
Parallel computation

high-performance computing, but interest in it has grown lately due to the physical constraints preventing frequency scaling.[35] As power consumption (and consequently heat generation) by computers has become a concern in recent years,[36] parallel computing has become the dominant paradigm in computer architecture, mainly in the form of multi-core processors.[37]

Communication and synchronization
between the different subtasks are typically some of the greatest obstacles to getting good parallel program performance.

The maximum possible speed-up of a single program as a result of parallelization is known as Amdahl's law.

Programming language theory and program semantics

Main articles:
Program semantics

Programming language theory is a branch of computer science that deals with the design, implementation, analysis, characterization, and classification of programming languages and their individual features. It falls within the discipline of theoretical computer science, both depending on and affecting mathematics, software engineering, and linguistics. It is an active research area, with numerous dedicated academic journals.

In

platform, hence creating a model of computation
.

Quantum computation

Main article:
Quantum computation

A

space–time in 1968.[43]

As of 2014[update], quantum computing is still in its infancy but experiments have been carried out in which quantum computational operations were executed on a very small number of qubits.[44] Both practical and theoretical research continues, and many national governments and military funding agencies support quantum computing research to develop quantum computers for both civilian and national security purposes, such as cryptanalysis.[45]

Symbolic computation

Main article:
Symbolic computation

floating point numbers, while symbolic computation emphasizes exact computation with expressions containing variables
that have not any given value and are thus manipulated as symbols (therefore the name of symbolic computation).

indefinite integration
, etc.

Very-large-scale integration

Main article:
VLSI

RAM and other glue logic
. VLSI allows IC makers to add all of these circuits into one chip.

Organizations

Journals and newsletters

Conferences

See also

Notes

  1. ^ "SIGACT". Retrieved 2017-01-19.
  2. ISBN 978-1-4503-7464-4
    .
  3. ^ "Any classical mathematical algorithm, for example, can be described in a finite number of English words". Rogers, Hartley Jr. (1967). Theory of Recursive Functions and Effective Computability. McGraw-Hill. Page 2.
  4. ^ Well defined with respect to the agent that executes the algorithm: "There is a computing agent, usually human, which can react to the instructions and carry out the computations" (Rogers 1967, p. 2).
  5. ^ "an algorithm is a procedure for computing a function (with respect to some chosen notation for integers) ... this limitation (to numerical functions) results in no loss of generality", (Rogers 1967, p. 1).
  6. zero or more inputs, i.e., quantities
    which are given to it initially before the algorithm begins" (Knuth 1973:5).
  7. ^ "A procedure which has all the characteristics of an algorithm except that it possibly lacks finiteness may be called a 'computational method'" (Knuth 1973:5).
  8. ^ "An algorithm has one or more outputs, i.e. quantities which have a specified relation to the inputs" (Knuth 1973:5).
  9. ^ Whether or not a process with random interior processes (not including the input) is an algorithm is debatable. Rogers opines that: "a computation is carried out in a discrete stepwise fashion, without the use of continuous methods or analog devices . . . carried forward deterministically, without resort to random methods or devices, e.g., dice" (Rogers 1967, p. 2).
  10. ^ "NIH working definition of bioinformatics and computational biology" (PDF). Biomedical Information Science and Technology Initiative. 17 July 2000. Archived from the original (PDF) on 5 September 2012. Retrieved 18 August 2012.
  11. ^ "About the CCMB". Center for Computational Molecular Biology. Retrieved 18 August 2012.
  12. ^ Rivest, Ronald L. (1990). "Cryptology". In J. Van Leeuwen (ed.). Handbook of Theoretical Computer Science. Vol. 1. Elsevier.
  13. ^ Bellare, Mihir; Rogaway, Phillip (21 September 2005). "Introduction". Introduction to Modern Cryptography. p. 10.
  14. ISBN 978-0-8493-8523-0
    .
  15. Dictionary of Algorithms and Data Structures. U.S. National Institute of Standards and Technology. 15 December 2004. Online version
    Accessed May 21, 2009.
  16. ^ Entry data structure in the Encyclopædia Britannica (2009) Online entry accessed on May 21, 2009.
  17. ^
    ISBN 978-0-132-14301-1
    .
  18. ^ Andrews (2000). Dolev (2000). Ghosh (2007), p. 10.
  19. ^ R. W. Butler (2001-08-06). "What is Formal Methods?". Retrieved 2006-11-16.
  20. ^ C. Michael Holloway. "Why Engineers Should Consider Formal Methods" (PDF). 16th Digital Avionics Systems Conference (27–30 October 1997). Archived from the original (PDF) on 16 November 2006. Retrieved 2006-11-16.
  21. ^ Monin, pp.3–4
  22. ISBN 978-0262681087
    .
  23. S2CID 2138288
    .
  24. ^ Rando Allikmets, Wyeth W. Wasserman, Amy Hutchinson, Philip Smallwood, Jeremy Nathans, Peter K. Rogan, Thomas D. Schneider, Michael Dean (1998) Organization of the ABCR gene: analysis of promoter and splice junction sequences, Gene 215:1, 111–122
  25. ISBN 978-0-387-95364-9
    .
  26. S2CID 17870175
    .
  27. ^ Charles H. Bennett, Ming Li, and Bin Ma (2003) Chain Letters and Evolutionary Histories Archived 2007-10-07 at the Wayback Machine, Scientific American 288:6, 76–81
  28. ^ David R. Anderson (November 1, 2003). "Some background on why people in the empirical sciences may want to better understand the information-theoretic methods" (PDF). Archived from the original (PDF) on July 23, 2011. Retrieved 2010-06-23.
  29. doi:10.1023/A:1007411609915
    .
  30. ^
    ISBN 978-0-387-31073-2
    .
  31. ^ Wernick, Yang, Brankov, Yourganov and Strother, Machine Learning in Medical Imaging, IEEE Signal Processing Magazine, vol. 27, no. 4, July 2010, pp. 25–38
  32. ^ Mannila, Heikki (1996). Data mining: machine learning, statistics, and databases. Int'l Conf. Scientific and Statistical Database Management. IEEE Computer Society.
  33. ^ Friedman, Jerome H. (1998). "Data Mining and Statistics: What's the connection?". Computing Science and Statistics. 29 (1): 3–9.
  34. ISBN 978-0-8053-0177-9
    .
  35. ^ S.V. Adve et al. (November 2008). "Parallel Computing Research at Illinois: The UPCRC Agenda" Archived 2008-12-09 at the Wayback Machine (PDF). Parallel@Illinois, University of Illinois at Urbana-Champaign. "The main techniques for these performance benefits – increased clock frequency and smarter but increasingly complex architectures – are now hitting the so-called power wall. The computer industry has accepted that future performance increases must largely come from increasing the number of processors (or cores) on a die, rather than making a single core go faster."
  36. ^ Asanovic et al. Old [conventional wisdom]: Power is free, but transistors are expensive. New [conventional wisdom] is [that] power is expensive, but transistors are "free".
  37. Asanovic, Krste et al. (December 18, 2006). "The Landscape of Parallel Computing Research: A View from Berkeley"
    (PDF). University of California, Berkeley. Technical Report No. UCB/EECS-2006-183. "Old [conventional wisdom]: Increasing clock frequency is the primary method of improving processor performance. New [conventional wisdom]: Increasing parallelism is the primary method of improving processor performance ... Even representatives from Intel, a company generally associated with the 'higher clock-speed is better' position, warned that traditional approaches to maximizing performance through maximizing clock speed have been pushed to their limit."
  38. ISBN 978-1-55860-428-5
    .
  39. Isaac L. Chuang
  40. ^ Manin, Yu. I. (1980). Vychislimoe i nevychislimoe [Computable and Noncomputable] (in Russian). Sov.Radio. pp. 13–15. Archived from the original on 10 May 2013. Retrieved 4 March 2013.
  41. S2CID 124545445
    .
  42. doi:10.1088/2058-7058/5/6/38
    .
  43. ^ Finkelstein, David (1968). "Space-Time Structure in High Energy Interactions". In Gudehus, T.; Kaiser, G. (eds.). Fundamental Interactions at High Energy. New York: Gordon & Breach.
  44. ^ "New qubit control bodes well for future of quantum computing". Retrieved 26 October 2014.
  45. ^ Quantum Information Science and Technology Roadmap for a sense of where the research is heading.
  46. ^ a b c d e The 2007 Australian Ranking of ICT Conferences Archived 2009-10-02 at the Wayback Machine: tier A+.
  47. ^ "MFCS 2017". Archived from the original on 2018-01-10. Retrieved 2018-01-09.
  48. ^ CSR 2018
  49. ^ a b c d e f g h i j The 2007 Australian Ranking of ICT Conferences Archived 2009-10-02 at the Wayback Machine: tier A.
  50. ^ FCT 2011 (retrieved 2013-06-03)

Further reading

  • quantification theory
    . Aimed at graduate students.

External links

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