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{{about|the branch of computer science and mathematics|the journal|Theoretical Computer Science (journal)}}
 
'''Theoretical computer science''' is a division or subset of general [[computer science]] and [[mathematics]] which focuses on more abstract or mathematical aspects of computing and includes the [[theory of computation]].
 
== Scope ==
It is not easy to circumscribe the theory areas precisely and the [[Association for Computing Machinery|ACM]]'s [[Special Interest Group on Algorithms and Computation Theory]] (SIGACT) describes its mission as the promotion of theoretical computer science and notes:<ref>{{cite web | title =  SIGACT | url = http://sigact.acm.org | accessdate = 2009-03-29}}</ref>
 
{{"|The field of theoretical computer science is interpreted broadly so as to include [[algorithms]], [[data structure]]s, [[computational complexity theory]], [[distributed computation]], [[parallel computation]], [[VLSI]], [[machine learning]], [[computational biology]], [[computational geometry]], [[information theory]], [[cryptography]], [[quantum computation]], [[computational number theory]] and [[Symbolic computation|algebra]], [[program semantics]] and [[Formal methods|verification]], [[automata theory]], and the study of [[randomness]]. Work in this field is often distinguished by its emphasis on mathematical technique and [[rigor#Mathematical rigour|rigor]].}}
 
To this list, the ACM's journal Transactions on Computation Theory adds [[coding theory]], [[computational learning theory]] and theoretical computer science aspects of areas such as [[databases]], [[information retrieval]], economic models and [[Computer network|networks]].<ref>{{cite web | title =  ToCT| url = http://toct.acm.org/journal.html | accessdate = 2010-06-09}}</ref> Despite this broad scope, the "theory people" in computer science self-identify as different from the "applied people." Some characterize themselves as doing the "(more fundamental) 'science(s)' underlying the field of computing."<ref>{{cite web | title = Challenges for Theoretical Computer Science: Theory as the Scientific Foundation of Computing | url = http://www.research.att.com/%7Edsj/nsflist.html#Intro | accessdate = 2009-03-29}}</ref> Other "theory-applied people" suggest that it is impossible to separate theory and application. This means, the so-called "theory people" regularly use experimental science(s) done in less-theoretical areas such as [[software system]] research. This also means, there is more cooperation than mutually exclusive competition between theory and application.
 
{| style="border:1px solid #ddd; text-align:center;  margin: 0 auto;" cellspacing="15"
| <math> P \rightarrow Q \,</math>
| [[File:DFAexample.svg|96px]]
| [[File:Elliptic curve simple.png|96px]]
| [[File:6n-graf.svg|96px]]
| [[File:Wang tiles.png|96px]]
| '''P = NP''' ?
|-
| [[Mathematical logic]]
| [[Automata theory]]
| [[Number theory]]
| [[Graph theory]]
| [[Computability theory]]
| [[Computational complexity theory]]
|-
| '''GNITIRW-TERCES'''
| <math>\Gamma\vdash x : Int</math>
| [[File:Commutative diagram for morphism.svg|96px]]
| [[File:SimplexRangeSearching.png|96px]]
| [[File:Blochsphere.svg|96px]]
|-
| [[Cryptography]]
| [[Type theory]]
| [[Category theory]]
| [[Computational geometry]]
| [[Quantum computer|Quantum computing theory]]
|}
 
== History ==
{{Main|History of computer science}}
 
While formal algorithms have existed for millennia ([[Euclid's algorithm]] for determining the [[greatest common divisor]] of two numbers is still used in computation), it was not until 1936 that [[Alan Turing]], [[Alonzo Church]] and [[Stephen Kleene]] formalized the definition of an algorithm in terms of computation. While binary and [[logical system]]s of mathematics had existed before 1703, when [[Gottfried Leibniz]] formalized logic with binary values for ''true'' and ''false''. While logical inference and mathematical proof had existed in ancient times, in 1931 [[Kurt Gödel]] proved with his [[incompleteness theorem]] that there were fundamental limitations on what statements could be proved or disproved.
 
These developments have led to the modern study of logic and [[computability]], and indeed the field of theoretical computer science as a whole. [[Information theory]] was added to the field with a 1948 mathematical theory of communication by [[Claude Shannon]]. In the same decade, [[Donald Hebb]] introduced a mathematical model of [[Hebbian learning|learning]] in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of [[neural network]]s and [[parallel distributed processing]] were established. In 1971, [[Stephen Cook]] and, working independently, [[Leonid Levin]], proved that there exist practically relevant problems that are [[NP-complete]] &ndash; a landmark result in [[computational complexity theory]].
 
With the development of [[quantum mechanics]] in the beginning of the 20th century came the concept that mathematical operations could be performed on an entire particle wavefunction. In other words, one could compute functions on multiple states simultaneously. This led to the concept of a [[quantum computer]] in the latter half of the 20th century that took off in the 1990s when [[Peter Shor]] showed that such methods could be used to factor large numbers in [[polynomial time]], which, if implemented, would render most modern [[public key cryptography]] systems uselessly insecure.
 
Modern theoretical computer science research is based on these basic developments, but includes many other mathematical and interdisciplinary problems that have been posed.
 
== Organizations ==
* [[European Association for Theoretical Computer Science]]
* [[SIGACT]]
 
== Journals and newsletters ==
* ''[[Information and Computation]]''
* ''[[Theory of Computing (journal)|Theory of Computing]]'' ([[Open access (publishing)|open access]] journal)
* ''[[Formal Aspects of Computing]]''
* ''[[Journal of the ACM]]''
* ''[[SIAM Journal on Computing]]'' (SICOMP)
* ''[[SIGACT News]]''
* ''[[Theoretical Computer Science (journal)|Theoretical Computer Science]]''
* ''[[Theory of Computing Systems]]''
* ''[[International Journal of Foundations of Computer Science]]''
* ''[[Chicago Journal of Theoretical Computer Science]]'' ([[Open access (publishing)|open access]] journal)
* ''[[Foundations and Trends in Theoretical Computer Science]]''
* ''[[Journal of Automata, Languages and Combinatorics]]''
* ''[[Acta Informatica]]''
* ''[[Fundamenta Informaticae]]''
* ''[[ACM Transactions on Computation Theory]]''
* ACM Transactions on Algorithms
* Information Processing Letters
 
== Conferences ==
* Annual ACM [[Symposium on Theory of Computing]] (STOC)<ref name="core-a-plus">The [http://www.core.edu.au/rankings/Conference%20Ranking%20Main.html 2007 Australian Ranking of ICT Conferences]: tier A+.</ref>
* Annual IEEE [[Symposium on Foundations of Computer Science]] (FOCS)<ref name="core-a-plus"/>
* ACM–SIAM [[Symposium on Discrete Algorithms]] (SODA)<ref name="core-a-plus"/>
* Annual [[Symposium on Computational Geometry]] (SoCG)<ref name="core-a">The [http://www.core.edu.au/rankings/Conference%20Ranking%20Main.html 2007 Australian Ranking of ICT Conferences]: tier A.</ref>
* [[International Colloquium on Automata, Languages and Programming]] (ICALP)<ref name="core-a"/>
* [[Symposium on Theoretical Aspects of Computer Science]] (STACS)<ref name="core-a"/>
* [[International Conference on Theory and Applications of Models of Computation]] (TAMC)
* [[European Symposium on Algorithms]] (ESA)<ref name="core-a"/>
* IEEE [[Symposium on Logic in Computer Science]] (LICS)<ref name="core-a-plus"/>
* [[International Symposium on Algorithms and Computation]] (ISAAC)<ref name="core-a"/>
* [[Workshop on Approximation Algorithms for Combinatorial Optimization Problems]] (APPROX)<ref name="core-a"/>
* [[Workshop on Randomization and Computation]] (RANDOM)<ref name="core-a"/>
* [[Computational Complexity Conference]] (CCC)<ref name="core-a"/>
* ACM [[Symposium on Parallelism in Algorithms and Architectures]] (SPAA)<ref name="core-a"/>
* ACM [[Symposium on Principles of Distributed Computing]] (PODC)<ref name="core-a-plus"/>
* [[International Symposium on Fundamentals of Computation Theory]] (FCT)<ref>[http://fct11.ifi.uio.no/ FCT 2011] (retrieved 2013-06-03)</ref>
 
==See also==
* [[Formal science]]
* [[Unsolved problems in computer science]]
* [[List of important publications in theoretical computer science]]
 
== Notes ==
<references/>
 
== Further reading ==
 
* [[Martin Davis]], Ron Sigal, Elaine J. Weyuker, ''Computability, complexity, and languages: fundamentals of theoretical computer science'', 2nd ed., Academic Press, 1994, ISBN 0-12-206382-1. Covers [[theory of computation]], but also [[program semantics]] and [[quantification theory]]. Aimed at graduate students.
 
== External links ==
* [http://www.sigact.org/webpages.php SIGACT directory of additional theory links]
* [http://theorymatters.org/ Theory Matters Wiki] Theoretical Computer Science (TCS) Advocacy Wiki
* [news://comp.theory Usenet comp.theory]
* [http://www.confsearch.org/confsearch/faces/pages/topic.jsp?topic=Theory&sortMode=1&graphicView=1 List of academic conferences in the area of theoretical computer science] at [http://www.confsearch.org confsearch]
* [http://cstheory.stackexchange.com/ Theoretical Computer Science - StackExchange], a Question and Answer site for researchers in theoretical computer science
* [http://www.csanimated.com/browse.php Computer Science Animated]
* http://theory.csail.mit.edu/  @ [[Massachusetts Institute of Technology]]
 
{{Computer science}}
 
{{DEFAULTSORT:Theoretical Computer Science}}
[[Category:Theoretical computer science|*]]
[[Category:Formal sciences]]

Revision as of 16:51, 31 October 2013

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Theoretical computer science is a division or subset of general computer science and mathematics which focuses on more abstract or mathematical aspects of computing and includes the theory of computation.

Scope

It is not easy to circumscribe the theory areas precisely and the ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) describes its mission as the promotion of theoretical computer science and notes:[1]

Template:"

To this list, the ACM's journal Transactions on Computation Theory adds coding theory, computational learning theory and theoretical computer science aspects of areas such as databases, information retrieval, economic models and networks.[2] Despite this broad scope, the "theory people" in computer science self-identify as different from the "applied people." Some characterize themselves as doing the "(more fundamental) 'science(s)' underlying the field of computing."[3] Other "theory-applied people" suggest that it is impossible to separate theory and application. This means, the so-called "theory people" regularly use experimental science(s) done in less-theoretical areas such as software system research. This also means, there is more cooperation than mutually exclusive competition between theory and application.

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

History

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While formal algorithms have existed for millennia (Euclid's algorithm for determining the greatest common divisor of two numbers is still used in computation), it was not until 1936 that Alan Turing, Alonzo Church and Stephen Kleene formalized the definition of an algorithm in terms of computation. While binary and logical systems of mathematics had existed before 1703, when Gottfried Leibniz formalized logic with binary values for true and false. While logical inference and mathematical proof had existed in ancient times, in 1931 Kurt Gödel proved with his incompleteness theorem that there were fundamental limitations on what statements could be proved or disproved.

These developments have led to the modern study of logic and computability, and indeed the field of theoretical computer science as a whole. Information theory was added to the field with a 1948 mathematical theory of communication by Claude Shannon. In the same decade, Donald Hebb introduced a mathematical model of learning in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of neural networks and parallel distributed processing were established. In 1971, Stephen Cook and, working independently, Leonid Levin, proved that there exist practically relevant problems that are NP-complete – a landmark result in computational complexity theory.

With the development of quantum mechanics in the beginning of the 20th century came the concept that mathematical operations could be performed on an entire particle wavefunction. In other words, one could compute functions on multiple states simultaneously. This led to the concept of a quantum computer in the latter half of the 20th century that took off in the 1990s when Peter Shor showed that such methods could be used to factor large numbers in polynomial time, which, if implemented, would render most modern public key cryptography systems uselessly insecure.

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

Organizations

Journals and newsletters

Conferences

See also

Notes

  1. ↑ Template:Cite web
  2. ↑ Template:Cite web
  3. ↑ Template:Cite web
  4. ↑ 4.0 4.1 4.2 4.3 4.4 The 2007 Australian Ranking of ICT Conferences: tier A+.
  5. ↑ 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 The 2007 Australian Ranking of ICT Conferences: tier A.
  6. ↑ FCT 2011 (retrieved 2013-06-03)

Further reading

External links

Template:Computer science

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