A Probabilistic Remark on Algebraic Program Testing

Until very recently, research in software reliability has divided quite neatly into two usually warring camps: methodologies with a mathematical basis and methodologies without such a basis. In the former view, “reliability” is identified wi+h “correctness” and the principle tocl has been formal and informal verification [ 11. In the latter view, “reliability” is taken to mean the ability to meet overall functional goals to within some predefmed limits [2,3 1. We have argued in [4] that the latter view holds a great deal of promise for further development at both the practical and analytical levels. Howden [5] proposes a first step in this direction by describing a method for “testing” a certain restricted class of programs wh.ose behavior can in a sense Howden makes precise :be ulgebraicized. In this way, “testing” a program is reduced to an equivalence test, the major compc~nents of which become (i) a combinatorial identification of “equivalent” structures; (ii) an algebraic test