Adaptive Homing is in P

Abstract

Homing preset and adaptive experiments with Finite State Machines (FSMs) are widely used when a non-initialized discrete event system is given for testing and thus, has to be set to the known state at the first step. The length of a shortest homing sequence is known to be exponential with respect to the number of states for a complete observable nondeterministic FSM while the problem of checking the existence of such sequence (Homing problem) is PSPACE-complete. In order to decrease the complexity of related problems, one can consider adaptive experiments when a next input to be applied to a system under experiment depends on the output responses to the previous inputs. In this paper, we study the problem of the existence of an adaptive homing experiment for complete observable nondeterministic machines. We show that if such experiment exists then it can be constructed with the use of a polynomial-time algorithm with respect to the number of FSM states.Comment: In Proceedings MBT 2015, arXiv:1504.0192

Deriving Homing Sequences for Finite State Machines with Timed Guards

“…Адаптивная установочная последовательность может быть построена по соответствующему установочному автомату [28,31], и далее мы адаптируем данный подход к синтезу кратчайшей временной адаптивной установочной последовательности для автомата с временными ограничениями S на основе конечно-автоматной абстракции.…”

Reducing the Complexity of Checking the Existence and Derivation of Adaptive Synchronizing Experiments for Nondeterministic FSMs

“…As each synchronizing test case is a homing test case with additional constraints, the existence check as well as the derivation of such test cases relies on such procedures for homing test cases. In (Kushik and Yevtushenko, 2015), it has been shown that when each state of a complete observable nondeterministic FSM can be initial, the existence of a homing test case can be checked in polynomial time. The procedure for deriving such test cases and potential heuristics improving the performance of the corresponding algorithm are discussed in (Kushik and Yenigun, 2015).…”

“…Not (Kushik and Yevtushenko, 2015). Represent them as as tree-like FSMs (where only the leaf nodes are allowed to have an indegree greater than 1) with terminal nodes r 1 , …, r n and designated deadlock state D, such that there exists a trace γ from the initial state of R jk to state r j if and only if {r j } is the γ-successor of the pair {s j , s k }.…”

“…Checking the existence of a homing test case R for a complete observable FSM S = (S, I, O, h S , S) can be performed in polynomial time (Kushik and Yevtushenko, 2015). On the other hand, the complexity of checking the existence of a d-transfer test case P(s, s′) for a state pair {s, s′} is polynomial as well.…”

Heuristics for Deriving Adaptive Homing and Distinguishing Sequences for Nondeterministic Finite State Machines

“…In this section, we discuss how to optimize the procedure for deriving an adaptive HS for an observable FSM S. The procedure is taken from [9] while the complexity of the related problem is given in [15]. The homing test case derivation strategy is based on the condition that each state pair of S is adaptively homing.…”