Foundation of Software Testing

The lack of a sound theoretical foundation has been a weakness of software testing for a long time. Although a number of approaches to this problem have been proposed and investigated, which have deepened our understanding of software testing, some most fundamental questions about software testing have not been satisfactorily answered at mathematical precision and accuracy. Since the late 1980’s, an axiomatic approach to the study of software testing was advanced, which shed a new light to the problem of foundation of software testing. The researches on this subject include:

  1. Based on Weyuker's axioms and the work of Baker et al., a set of axioms is proposed which have been successfully used to assess one of the most complicated classes of test criteria, the control flow test adequacy criteria.

  2. Software testing was investigated from the measurement perspective by application of the mathematical theory of measurement. A set of axioms was proposed. Its measurement theoretical properties (such as characteristics of admissible transformations, scale type and irregularity) and the logic properties (such as the relationship with Weyuker's axioms, the completeness and consistency of the axiom system) were proved.

  3. Given the fact that the nature of software testing is inductive inference, the axiom systems were interpreted by inductive inference, i.e. adequacy criteria were interpreted as convergence criteria of inductive inference. Such an interpretation results in new expressions of the relationship between software testing and software quality.

  4. The axioms for testing various types of software are being studied to characterise the specifal feature of the software, such as concurrent systems and distributed information systems. Testing methods are being derived from the axioms.

Related Publications

Gardiner, S. (ed.), Testing Safety Related Software, 1999. (Contribution to three chapters)

Zhu, H. and He, X., Constructions of Behaviour Observation Schemes in Software Testing, Proc. of The 5'th IEEE Symposium on High Assurance Systems Engineering, November 15-17, 2000, Albuquerque, New Mexico, in press. .

Zhu, H. and He, X., A theory of testing high-level Petri nets, Proc. of International Conference on Software – Theory and Practice, IFIP World Computer Congress 2000, Beijing, August 21-25, 2000, pp443~450.

Zhu, H. and Jin, L., The axiomatic approach to the foundation of software testing: an informal review, Post-Conference Proceedings of International Symposium on Computing and Microelectronics, Beijing, May 3, 1998.

Zhu, H., Toward a relationship between software reliability estimation and computational complexity, Chinese Journal of Software, Sept. 1998. (In Chinese)

Zhu, H. and Jin, L. Software Quality Assurance and Testing, Academic Press, Beijing, 1997.

Zhu, H., Hall, P. and May, J., Software unit test coverage and adequacy, ACM Computing Survey, Vol. 29, No. 4, Dec. 1997, pp366~427.

Jin, L., Zhu, H., and Hall, P., Adequate testing of hypertext applications, Journal of Information and Software Technology, UK. Vol. 39, No. 4, pp225-234, 1997.

Jin, L and Zhu, H., On adequacy criteria of testing hypertext applications, Chinese Journal of Software, August, 1997, pp130~136, (In Chinese).

Zhu, H., A formal interpretation of software testing as inductive inference, Journal of Software Testing, Verification and Reliability, UK., Vol. 6, July 1996, pp3~31.

Zhu, H., A formal analysis of the subsume relation between software test adequacy criteria, IEEE Transactions on Software Engineering, Vol. 22, No. 4, April 1996, pp248~255.

Zhu, H., Axiomatic assessment of control flow based software test adequacy criteria, Software Engineering Journal, UK, Sept. 1995.

Zhu, H., Hall, P., and May, J., Understanding software test adequacy -- An axiomatic and measurement approach, Mathematics of Dependable Systems, Edited by Mitchell, C., and Stavridou, V., Oxford University Press, 1995, pp275~295.

Zhu, H., An induction theory of software testing, Science in China, Supp. Vol. 38, Sept. 1995.

Zhu, H. and Jin, L. An inductive inference foundation of software testing, Proc. 5'th National Conference on Machine Learning, 1995.7. (In Chinese).

Jin, L., Zhu, H., and Hall, P., Testing hypertext for quality assurance, Proc. of SQM'95, Spain, May 1995.

Zhu, H. and Hall, P., Test data adequacy measurement, Software Engineering Journal, Vol. 8, No.1, Jan. 1993., pp12-30.

Zhu, H., Hall, P., and May, J., Inductive inference and software testing, Journal of Software Testing, Verification, and Reliability, Vol. 2, pp69-81, 1992.

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