Test vector

In computer science and engineering, a test vector is a set of inputs provided to a system in order to test that system. In software development, test vectors are a methodology of software testing and software verification and validation.

In computer science and engineering, a system acts as a computable function. An example of a specific function could be ${\displaystyle y=f(x)}${\displaystyle y=f(x)} where ${\displaystyle y}${\displaystyle y} is the output of the system and ${\displaystyle x}${\displaystyle x} is the input; however, most systems' inputs are not one-dimensional. When the inputs are multi-dimensional, we could say that the system takes the form ${\displaystyle y=f(x_{1},x_{2},...)}${\displaystyle y=f(x_{1},x_{2},...)} ; however, we can generalize this equation to a general form ${\displaystyle Y=C(X)}${\displaystyle Y=C(X)} where ${\displaystyle Y}${\displaystyle Y} is the result of the system's execution, ${\displaystyle C}${\displaystyle C} belongs to the set of computable functions, and ${\displaystyle X}${\displaystyle X} is an input vector. While testing the system, various test vectors must be used to examine the system's behavior with differing inputs.

For example, consider a login page with two input fields: a username field and a password field. In that case, the login system can be described as:

${\displaystyle y=L(u,p)}${\displaystyle y=L(u,p)}

with ${\displaystyle y\in \{true,false\}}${\displaystyle y\in \{true,false\}} and ${\displaystyle u,p\in \{String\}}${\displaystyle u,p\in \{String\}}, with ${\displaystyle true}${\displaystyle true} designating login successful, and ${\displaystyle false}${\displaystyle false} designating login failure, respectively.

Making things more generic, we can suggest that the function ${\displaystyle L}${\displaystyle L} takes input as a 2-dimensional vector and outputs a one-dimensional vector (scalar). This can be written in the following way:-

${\displaystyle Y=L(X)}${\displaystyle Y=L(X)}

with ${\displaystyle X=[x_{1},x_{2}]=[u,p]\;;\;Y=[y_{1}]}${\displaystyle X=[x_{1},x_{2}]=[u,p]\;;\;Y=[y_{1}]}

In this case, ${\displaystyle X}${\displaystyle X} is called the input vector, and ${\displaystyle Y}${\displaystyle Y} is called the output vector.

In order to test the login page, it is necessary to pass some sample input vectors ${\displaystyle \{X_{1},X_{2},X_{3},...\}}${\displaystyle \{X_{1},X_{2},X_{3},...\}}. In this context ${\displaystyle X_{i}}${\displaystyle X_{i}} is called a test vector.

Alternatively, the concatenation of ${\displaystyle X}${\displaystyle X} and ${\displaystyle Y}${\displaystyle Y}, e.g., ${\displaystyle [x_{1},x_{2},y_{1}]}${\displaystyle [x_{1},x_{2},y_{1}]}, can be called a test vector.

• Automatic test pattern generation

• Test Vector Guidelines. [1]
• Test Vector Considered Harmful. [2]

• Computer engineering
• Test items