Inferring Finite State Machines Without Reset Using State Identification Sequences

Adaptive Localizer Based on Splitting Trees

“…. The core trick, as already suggested by Hennie, is that after applying at most n + 1 times a sequence, the machine must have entered a cycle, and we proved [1] that another n − 2 applications were enough (in worst case) to identify where the machine is in the cycle, so as to predict the next application. After w 2n−1 1 the answer of the machine to w 1 can be predicted, so by applying w 2 we can know its answers to both w 1 and w 2 .…”

“…Hennie [2] and Kohavi [4] introduced approaches based on locating sequences, to build checking sequences, that can test for conformance. More recently, we introduced a localizer procedure to infer a FSM model of a black box system which cannot be reset [1] with two key assumptions: first, an upper bound n on the number of states, and second a characterization set (aka W -set) for the system. Whatever the initial state of the system, the application of the localizer will make it possible to ascertain the state reached at the end of it, or more precisely before applying the last characterizing sequence.…”

“…The main difficulty lies in the fact that each input sequence from the W -set must be applied after repeating a fixed number of times (2n − 1) a fixed sub-localizing sequence to ensure that the next iteration would be a repeated situation identifiable from the previous observations. The localizer procedure from [1] uses a fixed order of input sequences from the W -set to ensure that the same sequence is repeated at each level. With a splitting tree, the sequence to repeat may not be fixed.…”

“…This paves the way for new applications of localizing, in conformance testing or inference for non-resettable machines. In particular, it is possible to consider adapting an inference algorithm[1] so that the sequences separating subsets of states are discovered instead of being given. Thus it would be possible to infer incrementally with just a bound on the number of states, and with no initial knowledge of separating sequences for a black box system.Acknowledgments The authors acknowledge feedback from A. Petrenko.…”

Parallelizing Heuristics for Generating Synchronizing Sequences

“…However, sometimes such a reset input is not available, or even if it is available, it may be time consuming to apply the reset input. Therefore there are cases where the use of a reset input is not preferred [7][8][9].…”