Ordered t-way Combinations for Testing State-based Systems

Fault detection often depends on the specific order of inputs that establish states which eventually lead to a failure. However, beyond basic structural coverage metrics, it is often difficult to determine if the code has been exercised sufficiently to ensure confidence in its functions. Measures are needed to ensure that relevant combinations of input values have been tested with adequate diversity of ordering to ensure correct operation. Combinatorial testing and combinatorial coverage measures have been applied to many types of applications but have some deficiencies for verifying and testing state-based systems where the response depends on both input values and the current system state. In such systems, internal states change as input values are processed. Examples include network protocols, which may be in listening, partial connection, full connection, disconnected, and other states depending on the values of packet fields and the order of packets received. This paper discusses definitions for ordered t-way combination arrays and proves results regarding the construction of adequate blocks of test inputs, including consecutive ordering of combinations and with interleaving allowed. The application of the results to verify and test state- based systems is also illustrated.