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Metamorphic Testing

Metamorphic testing was originally developed, by others, as an approach to deriving new test
cases from an existing test suite, seeking to find additional bugs not found by the original tests.
Given a known execution function(input) produces output, the metamorphic properties of a
function (or of an entire application) enable automatic derivation of a new input’ from input such
that the expected output’ can be predicted from output. If the actual output’’ is different from
output’, then there is a flaw in the code or its documentation. We expanded metamorphic testing
in several ways, initially to apply to “non-testable programs”, where there is no test oracle; that
is, metamorphic testing can detect bugs even when we do not know whether output is correct for
input (so conventional testing techniques may not be useful). This problem arises for the
machine learning, data mining, search, simulation and optimization applications prevalent in “big
data” analysis. For example, if a machine learning program generates clusters from a set of
examples, one would expect it to produce the same clusters when the order of the input examples
is permuted; however, we have found anomalies in several widely used machine learning
libraries (e.g., Weka) where the result is different from expected when the set of input examples
is modified in some simple way. We are investigating how to extend the notion of metamorphic
properties to before and after state, beyond just input/output parameters, to find bugs that affect
the internal state but are not evident from input/output. Most recently we developed a tool for
automatically discovering candidate metamorphic properties from execution profiling that
performs better than student subjects; the state of the art is for a human domain expert to
manually define the properties, a tedious, error-prone and expensive process.

Team Members

Gail Kaiser

Graduate Students
Fang-Hsiang (“Mike”) Su

Former Graduate Students
Chris Murphy
Jonathan Bell



Fang-Hsiang Su, Jonathan Bell, Christian Murphy and Gail Kaiser. Dynamic Inference of Likely Metamorphic Properties to Support Differential Testing. 10th IEEE/ACM International Workshop on Automation of Software Test (AST), May 2015, pp. 55-59.

Jonathan Bell, Christian Murphy and Gail Kaiser. Metamorphic Runtime Checking of Applications Without Test Oracles. Crosstalk the Journal of Defense Software Engineering, 28(2):9-13, Mar/Apr 2015.

Christian Murphy, M. S. Raunak, Andrew King, Sanjian Chen, Christopher Imbriano, Gail Kaiser, Insup Lee, Oleg Sokolsky, Lori Clarke, Leon Osterweil. On Effective Testing of Health Care Simulation Software. 3rd International Workshop on Software Engineering in Health Care (SEHC), May 2011, pp. 40-47.

Xiaoyuan Xie, Joshua W. K. Ho, Christian Murphy, Gail Kaiser, Baowen Xu and Tsong Yueh Chen.  Testing and Validating Machine Learning Classifiers by Metamorphic Testing.  Journal of Systems and Software (JSS), Elsevier, 84(4):544-558, April 2011.

Christian Murphy, Kuang Shen and Gail Kaiser. Automatic System Testing of Programs without Test Oracles. International Symposium on Software Testing and Analysis (ISSTA), July 2009, pp. 189-200.

Christian Murphy, Kuang Shen and Gail Kaiser. Using JML Runtime Assertion Checking to Perform Metamorphic Testing in Applications without Test Oracles. 2nd IEEE International Conference on Software Testing, Verification and Validation (ICST), April 2009, pp. 436-445.

Christian Murphy, Gail Kaiser, Lifeng Hu and Leon Wu. Properties of Machine Learning Applications for Use in Metamorphic Testing. 20th International Conference on Software Engineering and Knowledge Engineering (SEKE), July 2008, pp. 867-872.

Christian Murphy, Gail Kaiser and Marta Arias. Parameterizing Random Test Data According to Equivalence Classes. 2nd ACM International Workshop on Random Testing (RT), November 2007, pp.38-41.

Christian Murphy, Gail Kaiser and Marta Arias. An Approach to Software Testing of Machine Learning Applications. 19th International Conference on Software Engineering and Knowledge Engineering (SEKE), July 2007, pp. 167-172.


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