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Additional resources for Techniques for automatic generation of tests from programs and specifications

Example text

In chapter 4 we analyze the complexity and incompleteness of una. Here we also present our alternative algorithm and a comparison between the two. Finally, in chapter 6 conclusions and future work are presented. g. x, r, and d. g. x(i) refers to vector x at iteration i. g. A. The notation ai· references the i:th row of A, while a·j means the j:th column. A matrix element at row i and column j in matrix A is denoted by aij . Here the problem of test data generation has the following form, Find subject to x = (x1 , .

The next solution x(1) is derived using b + s(1) . Running the system through our implementation of una, it gives us the solution x = 4 after 30 iterations. 4, which illustrates the three first iterations, we see that the direction vector becomes shorter for each iteration. This is why the step size between each Ax(i) gets smaller. With some fairly simple geometrical reasoning we can see that the angle between A and the two axes is directly coupled to the step size. 4 we have marked the angle between A and the e1 axis with α.

What’s more, if the columns of A are linearly dependent, an initial basis other than A must be found in order to meet the least square criterion. In other words, AT A must be invertible. If it is not, additional iterations for finding a feasible starting matrix must be performed. The simplex method, on the other hand, can be used to find an initial partition. Since we are not looking for an optimal solution, we are done once the initial basis is found. 5 shows that under some circumstances una does not find a solution.