# Enable Fair Proof-of-Work (PoW) Consensus for Blockchains in IoT by Miner Twins (MinT)
## 2 Related Work
### Digital Twins  
The concept of DT was proposed in 2002 and archived in a NASA white paper in 2014 [18]. Essentially, a DT is a digital representation of the components and dynamics of a physical system [19]. Based on the functionalities, DTs can be roughly categorized into three kinds: monitoring DTs, simulational DTs and operational DTs [20]. As suggested by the names, monitoring twins allow system operators to monitor the status of a physical system; simulation twins can predict the future status of the physical system in different scenarios using various simulation tools and ML algorithms; and operational twins is a _complex sensing and control system_ that enabled human operators to interact with a cyber-physical system and to perform different actions in addition to monitoring, analysis and prediction [21], which is similar to human-machine teaming [22]. Earlier studies on DT mainly focused on the area of manufacturing covering different key factors for smart manufacturing including simulation, optimization and the use of AI. For instance, an event-driven simulation for manufacturing and assembly tasks based on Digital Twin and human-robot collaboration was presented [23]. A DT-based framework was proposed to achieve high precision and multidisciplinary coupling during the assembly process, which mainly focused on High precision products (HPPs) workshops [24]. HPP also establishes a predict and optimization model as well as a case study to verify the effectiveness and feasibility. A case study presented an ice cream machine as an application example of DT in food industry [25], which focused on the visualization and interaction based on virtual reality (VR) and augmented reality (AR) technologies. Secure data transmission was also highlighted in the framework by employing a secure gate between machine and cloud. Recently, efforts are reported in variant aspects of smart cities including Smart Driving, Smart Grid and Smart Healthcare. For instance, the optimization issue in the electric propulsion drive systems (EPDS) of self-driving electric vehicles were discussed [26]. In the proposed DT-based framework, the connection between a logical twin in the control software with the propulsion motor drive system enables EPDS performance estimation. However, there were no experimental results presented after giving the concepts of the platform. A behaviors-based algorithm was proposed to help the drivers avoid potential risk [27]. Combining the ML techniques and DT relies on the connectivity of the system and faces challenges in optimization and accuracy [28]. A case study has been reported that tackles the management of wind farm using DT and cloud technologies combined with big data analysis to build remote control station [29]. Recently, some healthcare applications redefined DT by including living objects [30]. A DT-based healthcare framework was proposed for monitoring and predicting the health condition of an individual using wearable devices [31]. A DT-based remote surgery prototype was introduced consisting of VR, 4G and AI to create a digital twin of a patient and to realize real-time surgery over mobile network [32]. Due to the fast development of telecommunication technologies, 5G and beyond networks are very complicated as they are expected to support more emerging applications with more diverse requirements [33]. The community is considering DT as an efficient, cost-effective approach to accelerate the design, test and implementation of 5G/6G networks [34]. Due to the foreseeable importance and popularity of DT in IoT, 5G/6G and edge computing, blockchain is adopted to enhance the security, trust and reliability of DTs [11; 35]. The work reported in this paper, however, is the first in this area that leverages DT to tackle the unfair mining problem in the PoW consensus protocol. Using digital twins, MinT monitors the computing resource utility of the miners and quickly detects abusers using Singular Spectrum Analysis (SSA) [36], one of the fastest change point detection algorithms [37].