Fault-detection experiment with deterministic realizations and a nondeterministic model

Abstract

The algorithmic approach to the design of fault-detection experiments for testing of control devices requires a mathematical model that describes the behavior of the tested device and its reference model. A finite automaton usually provides a suitable mathematical model. The classical problem assumes that the reference model and the tested device behave as a deterministic f'mite automaton (in what follows, we use the term "automaton" for a deterministic f'mite automaton). The class of faults is limited to faults that do not increase the number of automaton states. It is also assumed that the experimenter has direct access to the inputs and outputs of the device being tested. The construction of multiple fault-detection experiments assumes the existence of an input symbol that allows the model automaton to return from any state to some fixed (initial) state. This special symbol remains a reset symbol under all faults [1]. Recent studies use a nondeterministic automaton (nd-automaton) as a reference model for testing. In particular, an ndautomaton is used to construct test cases that check computer network protocols for conformity [2-4]. It has been shown [5] that if the output of the device being tested is observable only on the output of another device, then a fault,detection experiment also can be constructed using a nondeterministic model. The construction of a fault-detection experiment usually focuses mainly on the design of input sequences. The set of admissible output responses is identified with the entire set of model output sequences. In this article we analyze the possibility of reducing the length of the fault-detection experiment by reducing the set of admissible output responses. The article is organized as follows. Section 1 introduces the main def'mitions and notation. Section 2 describes the possibility of reducing the admissible set of output sequences in a fault-detection experiment. Section 3 provides necessary and sufficient conditions for the realization of a nondeterministic automaton by a deterministic automaton. We examine the conditions that permit passing from the nd-automaton P to an nd-automaton P,~ with fewer states and fewer output responses. The set of automata realizing P is identical with the set of automata realizing P~.. We can thus construct a fault~etection experiment for the nd-automaton P based on the nd-automaton P~.. This possibility is illustrated in Section 4.