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Topic · Computational Theory and Mathematics

semigroups and automata theory

semigroups and automata theory is a research topic within Computational Theory and Mathematics. Science Explorer counts 25k research works in it since 1950. 13.5% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers topics in automata theory, formal languages, and combinatorics on words. It includes research on regular expressions, finite automata, transducers, synchronizing automata, Sturmian words, and state complexity. The cluster also explores the connections between automata theory and semigroups.

  • Automata
  • Formal Languages
  • Regular Expressions
  • Finite Automata
  • Combinatorics on Words
  • Transducers
  • Synchronizing Automata
  • Sturmian Words
  • State Complexity
  • Semigroups
Research works
25k
fractional, since 1950
In the world top 10%
3.3k
per year above
Top-10% rate
13.5%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
-16%
the tick is no change

Which countries lead semigroups and automata theory research?

By volume, the United States and France publish the most (302 and 183 works in 2022–2025).

By volume, 2022–2025

  1. 1 United States 302 works
  2. 2 France 183 works
  3. 3 China 169 works
  4. 4 Germany 157 works
  5. 5 Russia 138 works
  6. 6 United Kingdom 131 works
  7. 7 India 112 works
  8. 8 Japan 82 works
  9. 9 Italy 76 works
  10. 10 Canada 74 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

United States: 21.2%France: 12.8%China: 11.8%Germany: 11.0%6 others listed: 43.1%21%largest
United States302 · 21.2%France183 · 12.8%China169 · 11.8%Germany157 · 11.0%6 others listed613 · 43.1%

Shares of the rows listed above, not of the whole node.

Which institutions lead semigroups and automata theory research?

By volume in 2022–2025, Centre National de la Recherche Scientifique publishes the most semigroups and automata theory research, followed by University of Waterloo and Lomonosov Moscow State University.

By volume, 2022–2025

  1. 1 Centre National de la Recherche ScientifiqueFrance 30 works
  2. 2 University of WaterlooCanada 21 works
  3. 3 Lomonosov Moscow State UniversityRussia 17 works
  4. 4 University of OxfordUnited Kingdom 14 works
  5. 5 Czech Technical University in PragueCzechia 14 works
  6. 6 University of WarsawPoland 14 works
  7. 7 Justus-Liebig-Universität GießenGermany 14 works
  8. 8 Sobolev Institute of MathematicsRussia 13 works
  9. 9 St Petersburg UniversityRussia 13 works
  10. 10 Kazan Federal UniversityRussia 11 works

Who are the leading researchers in semigroups and automata theory?

The most-cited researchers publishing on semigroups and automata theory include Ronald L. Rivest, Vincent D. Blondel and Donald E. Knuth.

  1. 1 Ronald L. Rivest United States 7.3k citations
  2. 2 Vincent D. Blondel Belgium 4.4k citations
  3. 3 Donald E. Knuth United States 4k citations
  4. 4 Steven J. Miller United States 3.8k citations
  5. 5 Morteza Shamsizadeh Iran 3.6k citations
  6. 6 David Haussler United States 3.4k citations
  7. 7 N. J. A. Sloane United States 2.8k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

Where is semigroups and automata theory research done?

The largest centres of semigroups and automata theory research in 2022–2025 are Paris (France), Moscow (Russia), Prague (Czechia) and Beijing (China). Among places with at least 20 works in it, it is an unusually large share of all research in Waterloo.

Largest cities, 2022–2025

  1. 1 Paris France 59 works
  2. 2 Moscow Russia 52 works
  3. 3 Prague Czechia 28 works
  4. 4 Beijing China 25 works
  5. 5 Tokyo Japan 24 works
  6. 6 Warsaw Poland 23 works
  7. 7 Waterloo Canada 21 works
  8. 8 Novosibirsk Russia 18 works
  9. 9 Chennai India 16 works
  10. 10 Xi'an China 16 works

Where it is the local speciality

  1. WaterlooCA · 21.0 works14×
← less than its size predicts1×more →

Location quotient: how much more of its research is in semigroups and automata theory than the world average.

See semigroups and automata theory on the map

Where is the best place to study semigroups and automata theory?

Among universities, judged by research, Justus-Liebig-Universität Gießen, University of Warsaw and St Petersburg University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%5%10%mean 5.79%fractional works in this node (log) →share in the world top 10% →Justus-Liebig-Universität Gießen: 14, 9.0%University of Warsaw: 14, 8.0%St Petersburg University: 12, 5.3%Czech Technical University in Prague: 14, 6.1%University of Turku: 10, 6.8%University of Liège: 9, 6.2%University of Waterloo: 21, 0.3%University of St Andrews: 8, 5.3%University of Oxford: 14, 9.0%TU Wien: 9, 1.9%Justus-Liebig-Univer…University of WarsawCzech Technical Univ…St Petersburg Univer…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Justus-Liebig-Universität GießenGermany 69.59.0%29.5×14 +11.0%
2 University of WarsawPoland 65.48.0%12.6×14 +36.4%
3 St Petersburg UniversityRussia 64.05.3%12.5×12 +401.1%
4 Czech Technical University in PragueCzechia 58.66.1%27.3×14 -13.2%
5 University of TurkuFinland 56.96.8%17.0×10 -39.7%
6 University of LiègeBelgium 55.56.2%14.9×9 -12.6%
7 University of WaterlooCanada 48.10.3%17.9×21 -8.0%
8 University of St AndrewsUnited Kingdom 47.55.3%18.7×8 -45.5%
9 University of OxfordUnited Kingdom 46.89.0%5.2×14 -19.8%
10 TU WienAustria 46.51.9%14.1×9 +70.9%

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is semigroups and automata theory research growing?

Output in 2018–2022 was 16% lower than in 2013–2017, peaking in 2011.

19801990200020102020
grewheldshrank

The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.