Evaluating Length of a Shortest Adaptive Homing Sequence for Weakly Initialized FSMs

Abstract

There are many research papers devoted to the state identification problem of finite state machines (FSMs) which are widely used for analysis of discrete event systems. A deterministic complete reduced FSM always has a homing sequence (HS) but a number of non-deterministic FSMs not necessarily have a preset HS; nevertheless, those FSMs can still have an adaptive HS. Moreover, adaptive HS can be shorter than the preset. If each state can be an initial state of a complete FSM, i.e., an FSM is non-initialized, then a shortest adaptive HS (if it exists) has polynomial length in the number of FSM states. We show that it is not the case for weakly-initialized FSMs: such FSMs can have a shortest adaptive HS of exponential length in the number of FSM states / transitions. However, the experimental evaluation shows that the non-polynomial upper bound for a shortest adaptive HS was never reached for randomly generated weakly-initialized two-input FSMs.