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Algebraic program testing

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Summary

An approach to the study of program testing is introduced in which program testing is treated as a special kind of equivalence problem. In this approach, classes of programs P * and associated classes of test sets T * are defined which have the property that if two programs P and Q in P * agree on a set of tests from T *, then P and Q are computationally equivalent. The properties of a class P * and the associated class T * can be thought of as defining a set of assumptions about a hypothetical correct version Q of a program P in P *. If the assumptions are valid then it is possible to prove the correctness of P by testing. The main result of the paper is an equivalence theorem for classes of programs which carry out sequences of computations involving the elements of arrays.

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References

  1. Boyer, R.S., Elspas, B., Levitt, K.N.: SELECT—A formal system for testing and debugging programs by symbolic execution. In: Proceedings 1975 International Conference on Reliable Software, Los Angeles, pp. 234–245. Long Beach (Calif.): IEEE Press 1975

    Google Scholar 

  2. Caviness, B.F.: On canonical forms and simplification. Carnegie-Mellon University, Ph.D. Thesis, Department of Computer Science, 1968

  3. Clarke, L.A.: A system to generate test data and symbolically execute programs. IEEE Trans. Software Engrg. SE-2, 215–222 (1976)

    Google Scholar 

  4. COBOL-TDG-II: Information Management Incorporated, San Francisco, California

  5. Fairley, R.E.: An experimental program testing facility. IEEE Trans. Software Engrg. SE-1, 350–357 (1975)

    Google Scholar 

  6. Geller, M.: Test data as an aid in proving program correctness. In: Proceedings of Second Symposium on Principles of Programming Languages, Atlanta, pp. 209–218. New York: ACM Publications 1976

    Google Scholar 

  7. Goodenough, J.B., Gerhart, S.L.: Toward a theory of test data selection. IEEE Trans. Software Engrg. SE-1, 156–173 (1975)

    Google Scholar 

  8. Hetzel, W.C.: An experimental analysis of program verification methods. University of North Carolina, Ph.D. Thesis, Department of Computer Science, 1976

  9. Howden, W.E.: Elementary algebraic program testing techniques. University of California, San Diego, Applied Physics and Information Sciences Computer Science Technical Report 12, 1976

    Google Scholar 

  10. Howden, W.E.: Experiments with a symbolic evaluation system. AFIPS-76, pp. 899–908. Montvale (N.J.): AFIPS Press 1976

    Google Scholar 

  11. Howden, W.E.: Symbolic testing and the DISSECT symbolic evaluation system. IEEE Trans. Software Engrg. SE-3, 266–278 (1977)

    Google Scholar 

  12. Howden, W.E.: Methodology for the generation of program test data. IEEE Trans. Computers C-24, 554–560 (1975)

    Google Scholar 

  13. Howden, W.E.: Reliability of the path analysis testing strategy. IEEE Trans. Software Engrg. SE-2, 208–214 (1976)

    Google Scholar 

  14. Howden, W.E.: Symbolic testing and Lindenmayer grammars. Information Processing Lett. (to appear)

  15. Huang, J.C.: An approach to program testing. Comput. Surveys 7, 113–128 (1975)

    Google Scholar 

  16. King, J.C.: Symbolic execution and program testing. Comm. ACM 19, 385–394 (1976)

    Google Scholar 

  17. Krause, K.W., Smith, R.W., Goodwin, M.A.: Optimal software test planning through automated network analysis. In: Proceedings 1973 IEEE Symposium on Computer Software Reliability, Washington, pp. 18–22. Long Beach (Calif.): IEEE Press 1975

    Google Scholar 

  18. Miller, E.F., Melton, R.A.: Automated generation of testcase datasets. In: Proceedings 1975 International Conference on Reliable Software, Los Angeles, pp. 51–58. Long Beach (Calif.): IEEE Press 1975

    Google Scholar 

  19. Osterweil, L.J., Fosdick, L.D.: DAVE—A validation error detection and documentation system for Fortran programs. Software—Practice and Experience 6, 473–486 (1976)

    Google Scholar 

  20. Pimont, S., Rault, J.C.: A software reliability assessment based on a structural and behavioral analysis of program. In: Proceedings Second International Conference on Software Reliability, San Francisco, pp. 486–491. Long Beach (Calif.): IEEE Press 1976

    Google Scholar 

  21. Ramamoorthy, C.V., Ho, S.F.: Testing large software with automated software evaluation systems. IEEE Trans. Software Engrg. SE-1, 46–58 (1975)

    Google Scholar 

  22. Stucki, L.G.: Automatic generation of self-metric software. In: Proceedings of the 1973 IEEE Symposium on Computer Software Reliability, Washington, pp. 94–100. Long Beach (Calif.): IEEE Press 1973

    Google Scholar 

  23. Stucki, L.G., Foshee, G.D.: New assertion concepts for self-metric software validation. In: Proceedings of 1975 International Conference on Reliable Software. Los Angeles, pp. 59–71. Long Beach (Calif.): IEEE Press 1975

    Google Scholar 

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Author notes

  1. William E. Howden

    Present address: Department of Applied Physics and Information Science, University of California, 92093, San Diego, La Jolla, CA, USA

Authors and Affiliations

  1. University of Victoria, Victoria, Canada

    William E. Howden

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  1. William E. Howden
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Additional information

This research was funded by the National Science Foundation under grant No. MCS 76-03295

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Howden, W.E. Algebraic program testing. Acta Informatica 10, 53–66 (1978). https://doi.org/10.1007/BF00260923

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  • DOI: https://doi.org/10.1007/BF00260923

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