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Topic · Computational Theory and Mathematics

Formal Methods in Verification

Formal Methods in Verification is a research topic within Computational Theory and Mathematics. Science Explorer counts 43k research works in it since 1950. 9.9% of them reached the world's top 10% most cited for their field and year.

This cluster of papers revolves around formal methods in software verification and control, focusing on topics such as model checking, symbolic model checking, satisfiability modulo theories, temporal logic, hybrid systems, automata, safety verification, control barrier functions, runtime verification, and probabilistic systems.

  • Model Checking
  • Symbolic Model Checker
  • Satisfiability Modulo Theories
  • Temporal Logic
  • Hybrid Systems
  • Automata
  • Safety Verification
  • Control Barrier Functions
  • Runtime Verification
  • Probabilistic Systems
Research works
43k
fractional, since 1950
In the world top 10%
4.3k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
-12%
the tick is no change
Largest producer
United States
24% of the 10 largest, 2022-now
Formal Methods in Verification

Which countries lead Formal Methods in Verification research?

By volume, the United States and China publish the most (777 and 546 works in 2022-now).

By volume, 2022-now

  1. 1 United States 777 works
  2. 2 China 546 works
  3. 3 Germany 517 works
  4. 4 France 377 works
  5. 5 United Kingdom 281 works
  6. 6 Italy 237 works
  7. 7 Japan 150 works
  8. 8 Netherlands 137 works
  9. 9 India 123 works
  10. 10 Austria 105 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: 23.9%China: 16.8%Germany: 15.9%France: 11.6%6 others listed: 31.8%24%largest
United States777 · 23.9%China546 · 16.8%Germany517 · 15.9%France377 · 11.6%6 others listed1,033 · 31.8%

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

Which institutions lead Formal Methods in Verification research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Formal Methods in Verification research, followed by Helmholtz Association of German Research Centres and RWTH Aachen University.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 128 works
  2. 2 Helmholtz Association of German Research CentresGermany 47 works
  3. 3 RWTH Aachen UniversityGermany 41 works
  4. 4 Chinese Academy of SciencesChina 38 works
  5. 5 TU WienAustria 38 works
  6. 6 Eindhoven University of TechnologyNetherlands 35 works
  7. 7 University of OxfordUnited Kingdom 35 works
  8. 8 Technical University of MunichGermany 34 works
  9. 9 Carnegie Mellon UniversityUnited States 31 works
  10. 10 Max Planck SocietyGermany 30 works

Who are the leading researchers in Formal Methods in Verification?

The most-cited researchers publishing on Formal Methods in Verification include M. Weber, Aviv Regev and David H. Haussler.

  1. 1 M. Weber Israel 267k citations
  2. 2 Aviv Regev United States 236k citations
  3. 3 David H. Haussler United States 209k citations
  4. 4 Trevor William Robbins United Kingdom 199k citations
  5. 5 John Bannister Goodenough United States 175k 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 Formal Methods in Verification?

The most cited paper in Formal Methods in Verification is "Petri nets: Properties, analysis and applications" (Tadao Murata, 1989), with 10,641 citations. Next come "Graph-Based Algorithms for Boolean Function Manipulation" (8,956) and "Statecharts: a visual formalism for complex systems" (6,762).

Most cited papers
#PaperReleasedCitations
1 Petri nets: Properties, analysis and applications Tadao Murata · Proceedings of the IEEE Apr 1989 10,641
2 Graph-Based Algorithms for Boolean Function Manipulation Bryant · IEEE Transactions on Computers Open access Aug 1986 8,956
3 Statecharts: a visual formalism for complex systems David Harel · Science of Computer Programming Open access Jun 1987 6,762
4 A theory of timed automata Rajeev Alur, David L. Dill · Theoretical Computer Science Open access Apr 1994 6,524
5 Z3: An Efficient SMT Solver Leonardo de Moura, Nikolaj Bjørner · Lecture notes in computer science Conference paper 2008 6,516
All 98 most cited papers, with filters and sorting

Where is Formal Methods in Verification research done?

The largest centres of Formal Methods in Verification research in 2022-now are Beijing (China), Paris (France), Shanghai (China) and Munich (Germany). Among places with at least 20 works in it, it is an unusually large share of all research in Saarbrücken, Linz and Bremen.

Largest cities, 2022-now

  1. 1 BeijingChina 124 works
  2. 2 ParisFrance 111 works
  3. 3 ShanghaiChina 81 works
  4. 4 MunichGermany 73 works
  5. 5 SaarbrückenGermany 57 works
  6. 6 TokyoJapan 57 works
  7. 7 LondonUnited Kingdom 51 works
  8. 8 ViennaAustria 51 works
  9. 9 AachenGermany 42 works
  10. 10 Xi'anChina 39 works

Where it is the local speciality

  1. SaarbrückenDE · 57.3 works40×
  2. LinzAT · 21.0 works19×
  3. BremenDE · 30.9 works19×
  4. EindhovenNL · 36.1 works19×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Formal Methods in Verification than the world average.

See Formal Methods in Verification on the map

Where is the best place to study Formal Methods in Verification?

Among universities, judged by research, Macau University of Science and Technology, Ludwig-Maximilians-Universität München and Technical University of Munich 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%20%40%mean 17.94%fractional works in this field (log) →share of work in the world top 10% →Ludwig-Maximilians-U…Macau University of …Hong Kong University…Technical University…
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
1Macau University of Science and TechnologyChina 76.526.1%14.2×12 +61.9%
2Ludwig-Maximilians-Universität MünchenGermany 70.931.6%7.1×23 +10.0%
3Technical University of MunichGermany 63.218.9%10.2×34 -33.9%
4Hong Kong University of Science and TechnologyChina 62.425.3%7.2×11 +227.3%
5RWTH Aachen UniversityGermany 61.611.2%13.6×41 -0.1%
6Carnegie Mellon UniversityUnited States 61.414.0%19.6×31 -60.8%
7University of OxfordUnited Kingdom 61.210.4%6.5×35 -2.2%
8ETH ZurichSwitzerland 57.720.6%6.2×16 +0.9%
9TU WienAustria 57.69.5%32.6×38 -11.9%
10University of Colorado BoulderUnited States 57.311.8%10.6×18 +83.3%

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 Formal Methods in Verification, country by country

Is Formal Methods in Verification research growing?

Output in 2022-2025 was 12% lower than in 2018-2021, peaking in 2002.

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 Formal Methods in Verification as a percentage of every work published that year, 0.017% in 2024.

still counting0.050%0.10%0.15%Formal Methods in Verification0.017% in 202519801990200020102020

Fractional works of Formal Methods in Verification 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%Formal Methods in Verification10.0% 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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