Boundary-value analysis

Boundary value analysis is a software testing technique in which tests are designed to include representatives of boundary values in a range. The idea comes from the boundary. Given that we have a set of test vectors to test the system, a topology can be defined on that set. Those inputs which belong to the same equivalence class as defined by the equivalence partitioning theory would constitute the basis. Given that the basis sets are neighbors, there would exist a boundary between them. The test vectors on either side of the boundary are called boundary values. In practice this would require that the test vectors can be ordered, and that the individual parameters follows some kind of order (either partial order or total order).

Formally the boundary values can be defined as below:- Let the set of the test vectors be ${\displaystyle X_{1},\dots ,X_{n}}$. Let's assume that there is an ordering relation defined over them, as ${\displaystyle \leq }$. Let ${\displaystyle C_{1},C_{2}}$ be two equivalent classes. Assume that test vector ${\displaystyle X_{1}\in C_{1}}$ and ${\displaystyle X_{2}\in C_{2}}$. If ${\displaystyle X_{1}\leq X_{2}}$ or ${\displaystyle X_{2}\leq X_{1}}$ then the classes ${\displaystyle C_{1},C_{2}}$ are in the same neighborhood and the values ${\displaystyle X_{1},X_{2}}$ are boundary values.

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