Once Upon A Time In Software Testing

Test Execution

Successful execution of a test case $$ TC $$:

$$ I_{iut}\ {\bf passes}\ TC $$

It is easily extended to a test suite $$ TS $$:

$$ I_{iut}\ {\bf passes}\ TS \Leftrightarrow \forall\ TC \in TS : I_{iut}\ {\bf passes}\ TC $$

$$ I_{iut}\ {\bf fails}\ TC \Leftrightarrow I_{iut}\ \cancel{\bf passes} TC $$

Example

$$ L = (S, Act, \rightarrow) $$
with
$$ S = \lbrace s_{1}, s_{2}, s_{3}, s_{4} \rbrace $$
and
$$ Act = \lbrace COFFEE, TEA, BUTTON \rbrace $$

Example

$$ \begin{align} traces(s_{3}) = & \lbrace \\ & BUTTON, \\ & BUTTON \cdot TEA \cdot BUTTON, \\ & \dots \rbrace = traces(s_{1}) = traces(s_{4}) \\ \\ traces(s_{2}) = & \lbrace \\ & TEA, \\ & COFFEE, \\ & TEA \cdot BUTTON \cdot TEA, \\ & \dots \rbrace \end{align} $$

Input/Output LTS

By partitioning the actions labels ($$ Act $$) into inputs ($$ Act_{I} $$)
and outputs ($$ Act_{U} $$), we can obtain an IOLTS:

$$ Act = Act_{I} \cup Act_{U} $$

The names of input actions end on "$$ ? $$", and
those of output actions with "$$ ! $$".

We introduce a special action δ to denote quiescence.

Example

$$ \begin{align} Act_{I} = & \lbrace BUTTON?, COFFEE?, TEA? \rbrace \\ Act_{U} = & \lbrace COFFEE!, TEA! \rbrace \end{align} $$

Context (1/2)

Michelin relies on a method close to the Computer Integrated Manufacturing (CIM) approach to control its production:

These levels can exchange data among them.