Using Vapnik–Chervonenkis Dimension to Analyze the Testing Complexity of Program Segments

AbstractWe examine the complexity of testing different program constructs. We do this by defining a measure of testing complexity known as VCP-dimension, which is similar to the Vapnik–Chervonenkis dimension, and applying it to classes of programs, where all programs in a class share the same syntactic structure. VCP-dimension gives bounds on the number of test points needed to determine that a program is approximately correct, so by studying it for a class of programs we gain insight into the difficulty of testing the program construct represented by the class. We investigate the VCP-dimension of straight line code, if–then–else statements, and for loops. We also compare the VCP-dimension of nested and sequential if–then–else statements as well as that of two types of for loops with embedded if–then–else statements. Finally, we perform an empirical study to estimate the expected complexity of straight line code