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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. 10.0% 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%
2.5k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+0%
the tick is no change
Largest producer
United States
21% of the 10 largest, 2022-now
semigroups and automata theory

Which countries lead semigroups and automata theory research?

By volume, the United States and France publish the most (335 and 198 works in 2022-now).

By volume, 2022-now

  1. 1 United States 335 works
  2. 2 France 198 works
  3. 3 China 194 works
  4. 4 Germany 169 works
  5. 5 Russia 150 works
  6. 6 United Kingdom 140 works
  7. 7 India 127 works
  8. 8 Japan 93 works
  9. 9 Italy 84 works
  10. 10 Canada 80 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: 21.3%France: 12.6%China: 12.4%Germany: 10.8%6 others listed: 42.9%21%largest
United States335 · 21.3%France198 · 12.6%China194 · 12.4%Germany169 · 10.8%6 others listed675 · 42.9%

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

Which institutions lead semigroups and automata theory research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most semigroups and automata theory research, followed by Russian Academy of Sciences and University of Waterloo.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 90 works
  2. 2 Russian Academy of SciencesRussia 36 works
  3. 3 University of WaterlooCanada 23 works
  4. 4 Lomonosov Moscow State UniversityRussia 18 works
  5. 5 University of OxfordUnited Kingdom 15 works
  6. 6 University of WarsawPoland 15 works
  7. 7 Justus-Liebig-Universität GießenGermany 15 works
  8. 8 St Petersburg UniversityRussia 15 works
  9. 9 Czech Technical University in PragueCzechia 15 works
  10. 10 University of TurkuFinland 11 works

Who are the leading researchers in semigroups and automata theory?

The most-cited researchers publishing on semigroups and automata theory include David H. Haussler, H. Vincent Poor and Eugene Wimberly Myers.

  1. 1 David H. Haussler United States 209k citations
  2. 2 H. Vincent Poor United States 165k citations
  3. 3 Eugene Wimberly Myers Germany 163k citations
  4. 4 Noam Chomsky United States 141k citations
  5. 5 Claude E. Shannon United States 138k citations

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

What are the most cited papers in semigroups and automata theory?

The most cited paper in semigroups and automata theory is "Reducibility among Combinatorial Problems" (Richard M. Karp, 1972), with 11,108 citations. Next come "Communication and Concurrency" (6,871) and "The complexity of theorem-proving procedures" (6,257).

Most cited papers
#PaperReleasedCitations
1 Reducibility among Combinatorial Problems Richard M. Karp Book chapter 1972 11,108
2 Communication and Concurrency Robin Milner 1989 6,871
3 The complexity of theorem-proving procedures Stephen A Cook Conference paperOpen access 1971 6,257
4 On observing nondeterminism and concurrency Matthew Hennessy, Robin Milner · Lecture notes in computer science Conference paper 1980 4,501
5 Efficient string matching Alfred V. Aho, Margaret J. Corasick · Communications of the ACM Jun 1975 2,969
All 100 most cited papers, with filters and sorting

Where is semigroups and automata theory research done?

The largest centres of semigroups and automata theory research in 2022-now 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-now

  1. 1 ParisFrance 66 works
  2. 2 MoscowRussia 59 works
  3. 3 PragueCzechia 30 works
  4. 4 BeijingChina 28 works
  5. 5 TokyoJapan 28 works
  6. 6 WarsawPoland 25 works
  7. 7 WaterlooCanada 23 works
  8. 8 NovosibirskRussia 18 works
  9. 9 Xi'anChina 18 works
  10. 10 GiessenGermany 17 works

Where it is the local speciality

  1. WaterlooCA · 23.2 works15×
← 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, University of Oxford, University of Waterloo and University of Cambridge 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%10%20%mean 13.99%fractional works in this field (log) →share of work in the world top 10% →University of Cambri…University of Manche…University of OxfordUniversity of Waterloo
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1University of OxfordUnited Kingdom 69.414.0%5.3×15 +1.5%
2University of WaterlooCanada 65.44.1%20.4×23 +14.1%
3University of CambridgeUnited Kingdom 65.018.9%3.9×10 +462.4%
4University of ManchesterUnited Kingdom 64.018.2%6.2×11 +303.7%
5Ural Federal UniversityRussia 60.019.1%18.0×11 -2.6%
6University of WarsawPoland 57.317.3%14.5×15 -30.1%
7Universidade do PortoPortugal 57.314.8%8.3×11 +25.8%
8University of LiègeBelgium 56.012.1%14.7×10 +14.9%
9Massachusetts Institute of TechnologyUnited States 54.314.4%6.2×9 -9.4%
10Czech Technical University in PragueCzechia 49.37.0%30.2×15 +36.4%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in semigroups and automata theory, country by country

Is semigroups and automata theory research growing?

Output in 2022-2025 was 0% higher than in 2018-2021, peaking in 2011. The fastest-growing topics are semigroups and automata theory.

still counting19801990200020102020
grewheldshrank

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

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is semigroups and automata theory as a percentage of every work published that year, 0.0099% in 2024.

still counting0.025%0.050%0.075%semigroups and automata theory0.0090% in 202519801990200020102020

Fractional works of semigroups and automata theory over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%semigroups and automata theory9.9% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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.

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