Combinatorial Methods for Trust and Assurance

Combinatorial methods reduce costs for testing, and have important applications in software engineering:  

• Combinatorial or t-way testing is a proven method for better testing at lower cost. The key insight underlying its effectiveness resulted from a series of studies by NIST from 1999 to 2004. NIST research showed that most software bugs and failures are caused by one or two parameters, with progressively fewer by three or more, which means that combinatorial testing can provide more efficient fault detection than conventional methods. Multiple studies have shown fault detection equal to exhaustive testing with a 20X to 700X reduction in test set size.  New algorithms compressing combinations into a small number of tests have made this method practical for industrial use, providing better testing at lower cost. See articles on high assurance software testing or security and reliability. 
• Assured autonomy and AI/ML verification:  Input space coverage measurements are needed in assurance and verification of autonomous systems, because current methods for assurance of safety critical systems rely on measures of structural coverage, which do not apply to many autonomous systems. Combinatorial methods, including a theorem relating measures of input space coverage, offer a better approach for autonomous system verification and AI assurance. 
  Assured Autonomy through Combinatorial Methods - keynote talk from
  6th IEEE Dependable and Secure Computing conference, Nov 7-9, 2023 at University of South Florida.
• NIST Tech reports on coverage measurement for assured autonomy:
  - Ordered t-way Combinations for Testing State-based Systems (paper)
        Presentation:   Powerpoint    Video (mp4)
  - Combination Frequency Differencing
  - Combinatorial Coverage Difference Measurement

ACTS - award winning tool for combinatorial testing, used in thousands of organizations worldwide. 
- The ACTS tool was the subject of the Most Influential Paper award at ICST 2023 (Practical category), Yu, L., Lei, Y., Kacker, R. N., & Kuhn, D. R. "ACTS: A combinatorial test generation tool" 2013 IEEE Sixth International Conference on Software Testing, Verification and Validation (ICST)
- ACTS development team received the Excellence in Technology Transfer Award, 2009, Federal Laboratory Consortium Mid-Atlantic Region

Examples and Case Studies - from some of the world's largest organizations, including Adobe, Avaya, Bosch, IBM, Jaguar Land Rover, Lockheed Martin, Mercedes Benz, US Nuclear Regulatory Commission, Red Hat, Rockwell Collins, Siemens, the US Air Force, US Army, US Marine Corps, US Navy, and others. 
     - Industrial examples -       - Autonomous systems -       - Cybersecurity -

FREELY AVAILABLE SOFTWARE    More than 4,500 corporate and university users   --> ACTS 3.3 is the latest version of the covering array generator 
Software on this site is free of charge and will remain free in the future. It is public domain; no license is required and there are no restrictions on use. You are free to include it and redistribute it in commercial products if desired. NIST is a US Government agency, doing research in advanced measurement and test methods. 
To obtain the tools, please send a request to Rick Kuhn - kuhn@nist.gov.  Please provide first and last name, and organization.  We will send you a download link. 

QUICK START - It's easy to learn the basics of this method!    

• Tutorial (pdf in English or Español):  Practical Combinatorial Testing // Pruebas Combinatorias Prácaticas
• Brief overview (12:46, mp4) of why it's so effective 
• Tutorial presentation (pdf) from the 2019 Defense and Aerospace Test and Analysis Workshop 

Teaching workshops and short courses conducted jointly with Virginia Tech
- Defense and Aerospace Test and Analysis Workshop (April 22, 2025)
- Combinatorial Testing for AI-Enabled Systems (Sept 4, 2024)

New papers:

• Kuhn, D. R., Raunak, M. S., Kacker, R. N., Chandrasekaran, J., Lanus, E., Cody, T., & Freeman, L. (2024). Assured Autonomy Through Combinatorial Methods. Computer, 57(5), 86-90.
• M S Raunak, D R Kuhn, R N Kacker, Jeff Y Lei, Combinatorial Testing for Reliable Systems, IEEE Reliability Magazine, vol 1, issue 1, Feb 2024, DOI: 10.1109/MRL.2024.3355874
• M. Olsen, M S Raunak, D.R. Kuhn, Predicting ABM Results with Covering Arrays and Random Forests, International Conference on Computational Science,  Prague, Czech Republic, 3-5 July, 2023.
• D. R. Kuhn, M S Raunak, R.N. Kacker, Ordered t-way Combinations for Testing State-based Systems, IEEE 16th Intl Conf on Software Testing, Verification and Validation Workshops, 2023
• K. Khadka, J. Chandrasekaran, J.Y. Lei, R. Kacker, R. Kuhn, Synthetic Data Generation Using Combinatorial Testing and Variational Autoencoder,  IEEE 16th Intl Conf on Software Testing, Verification and Validation Workshops, 2023 
• B. Garn, D. Schreiber, D. Simos, R. Kuhn, J. Voas, R. Kacker, Summary of Combinatorial Methods for Testing Internet of Things Smart Home Systems, IEEE 16th Intl Conf on Software Testing, Verification and Validation Workshops, 2023

SOME OF OUR ACCOMPLISHMENTS TO DATE INCLUDE:

• Empirical finding that software failures are triggered by interactions of only a few variables (1 to 6)
• IPOG covering array algorithm and its variants, more efficient than other known algorithms
• Developed sequence covering arrays, extending combinatorial methods to event sequence testing
• Measurement science and tools for combinatorial coverage
• Theorem relating (static) combinatorial input space coverage to (dynamic) structural code coverage, and
• Methods for error detection without conventional test oracle

Contacts:  Rick Kuhn  - kuhn@nist.gov, or Raghu Kacker - raghu.kacker@nist.gov  or M S Raunak - ms.raunak@nist.gov