It has been proved that each class is strictly included into the next. For instance, testing when we assume that the behavior of the implementation under test can be denoted by a deterministic finite-state machine for some known finite sets of inputs and outputs and with some known number of states belongs to Class I (and all subsequent classes). However, if the number of states is not known, then it only belongs to all classes from Class II on. If the implementation under test must be a deterministic finite-state machine failing the specification for a single trace (and its continuations), and its number of states is unknown, then it only belongs to classes from Class III on. Testing temporal machines where transitions are triggered if inputs are produced within some real-bounded interval only belongs to classes from Class IV on, whereas testing many non-deterministic systems only belongs to Class V (but not all, and some even belong to Class I). The inclusion into Class I does not require the simplicity of the assumed computation model, as some testing cases involving implementations written in any programming language, and testing implementations defined as machines depending on continuous magnitudes, have been proved to be in Class I. Other elaborated cases, such as the testing framework by Matthew Hennessy under must semantics, and temporal machines with rational timeouts, belong to Class II.
If the number of states are unknown and the finite state of the machine is failing for a single trace, which group does this fall into?
Class III

The Sultanate of Ifat, led by the Walashma dynasty with its capital at Zeila, ruled over parts of what is now eastern Ethiopia, Djibouti, and northern Somalia. The historian al-Umari records that Ifat was situated near the Red Sea coast, and states its size as 15 days travel by 20 days travel. Its army numbered 15,000 horsemen and 20,000 foot soldiers. Al-Umari also credits Ifat with seven "mother cities": Belqulzar, Kuljura, Shimi, Shewa, Adal, Jamme and Laboo.
What dynasty ruled the Sultanate of Ifat?
the Walashma dynasty

The astronomer Aristarchus of Samos was the first known person to propose a heliocentric model of the solar system, while the geographer Eratosthenes accurately calculated the circumference of the Earth. Hipparchus (c. 190 c. 120 BC) produced the first systematic star catalog. The level of achievement in Hellenistic astronomy and engineering is impressively shown by the Antikythera mechanism (150-100 BC), an analog computer for calculating the position of planets. Technological artifacts of similar complexity did not reappear until the 14th century, when mechanical astronomical clocks appeared in Europe.
Who created the sun-centered model of the solar system?
Aristarchus of Samos