Abstract
State identification is a long standing problem in the area of Finite State Machine (FSM) based modeling and testing of discrete event systems. For the identification of the current state of the system, so-called homing and synchronizing experiments with FSMs are used whereas for the initial state identification one can perform a distinguishing experiment. The homing, synchronizing, and distinguishing experiments are known as “gedanken” experiments, and the sequences for these experiments can be derived for deterministic and nondeterministic, partial and complete specification FSMs that are used to formally represent the required behavior of systems under investigation. The problems of checking the existence and derivation of homing, synchronizing, and distinguishing sequences are known to become harder as a specification FSM turns to be nondeterministic and partial. It is also known that in some cases the complexity can be reduced through a ‘switch’ from preset to adaptive experiment derivation. In this paper, we study how the partiality and adaptivity affect the complexity of checking the existence of homing/synchronizing/distinguishing sequences for deterministic and nondeterministic FSMs and visualize the complexity issues via appropriate figures. We also mention that the existing solutions to state identification problems are widely used for verification and testing of finite state transition systems.
Highlights
The state identification problem using gedanken experiments with Finite State Machines (FSMs) is a long standing problem
We study how the partiality and adaptivity affect the complexity of checking the existence of homing/synchronizing/distinguishing sequences for deterministic and nondeterministic FSMs and visualize the complexity issues via appropriate figures
We have considered the problems of checking the existence of homing, synchronizing, and distinguishing experiments for various FSM types, namely, for complete and partial, deterministic and nondeterministic FSMs
Summary
The state identification problem using gedanken experiments with Finite State Machines (FSMs) is a long standing problem. For nondeterministic complete observable FSMs, checking the existence of a preset homing/synchronizing/distinguishing sequence is PSPACE-complete [5, 6, 15] and in this paper, we show that it is the same for partial machines. For nondeterministic complete FSMs the adaptivity reduces the complexity of the problem of checking the existence of a homing/synchronizing sequence as the problem ‘falls into’ P [8, 13]. All the results on the complexity of the existence check of homing/synchronizing/distinguishing sequences for deterministic and nondeterministic, complete and partial FSMs are collected together and the complexity issues are visualized via appropriate figures. We close some gaps in the area, in particular, we show that differently from deterministic machines the adaptivity does not help to reduce the complexity of adaptive distinguishing experiments for nondeterministic 2-input FSMs. The structure of the paper is as follows.
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