Adaptive Homing is in P

TL;DR

This paper demonstrates that for complete observable nondeterministic finite state machines, the existence of an adaptive homing experiment can be decided and constructed efficiently using a polynomial-time algorithm.

Contribution

It proves that the problem of finding adaptive homing experiments for such systems is solvable in polynomial time, reducing complexity compared to traditional methods.

Findings

Existence of adaptive homing experiments can be decided in polynomial time.

Constructive polynomial-time algorithm for adaptive homing experiments.

Reduces complexity of homing problem for nondeterministic FSMs.

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.