# Multiple-Valued Logic Modelling for Agents Controlled via Optical Networks
## 1 Introduction
### Mobile Robotic Agents and Position-Based Cryptography Schemes
The prover \(P\) measures \(x_{1},x_{2}\), calculates the \(XOR\) operation \(x_{1}\oplus x_{2}\) and further calculates the random hash function \(H(x_{1}\oplus x_{2})\), using  
Figure 2: The principal scheme of quantum route verification of a mobile agent M, uniting methods proposed in [32,79]. the RO module [22; 77]. After this, the prover \(P\) has the correct basis for the measurement of the classical value \(\widetilde{q}\) of the qubit \(\mid\!\Psi\!\!>\). Further, \(P\) simultaneously sends measured \(\widetilde{q}\) by its EPR source to a pair of verifiers located along one axis (the details of the selection of necessary bits were not set by the protocol). If both photons were sent simultaneously by one entangled photon pair, their classical values obtained by the verifier modules will be equal (for equal distances), accurate to the sign. Then, position verification is successful, and further steps can be performed. In fact, the choice of EPR scheme by [PERSON] [33] was determined by the necessity to simultaneously emit entangled photons along space axes, as the minimal time interval between the detection of two these photons guarantees the advantage for the protocol PU. That is why the protocol PU is limited by light polarization scheme. However, one should note that although the protocol PU principally used a wireless atmospheric data line, the EPR scheme [75] can also be used in the fiber optics quantum line. After successful position verification, the second step of the procedure is to generate a random key, secretly distributed by the EPR source between the agent \(P\) and the visited checkpoint. Thus, during the passing of the route, agent \(P\) will accumulate random keys \(K_{1},\ldots,K_{q}\), and each visited checkpoint will have only one of keys \(K_{1},\ldots,K_{q}\). In order to approve the route passing to the final checkpoint, the agent \(P\) declares its set of keys, as the checkpoint chooses some of keys for verification and requests their copies via the trusted network. Then, the final checkpoint compares the declared keys with their network's replicas. For access to the requested service, agent \(P\) should also additionally pass another check step, based on the comparison of the digital image obtained during the route passing and declared by \(P\), with its replica transferred from a distant neural network database [32]. The main result of the paper [32] was that both the quantum protocol PU and template digital image taken from a neural network were represented by multiple-valued logic expressions attributed to time scale. Such a model has considered the joint work of the prover \(P\) with the verifier as the interaction of two agents, described by separate AGA functions. However, the drawback of verification schemes [32; 79] was that all involved checkpoints were considered as trusted nodes, because:  
* classical data in protocol PU are transferred without errors, although the acceptable quantum channel error in this protocol was estimated as 3.5%;
* checkpoints are supposed to exchange accumulated keys and neural network data without errors and limitations. Such a scheme, including stationary trusted servers with QKD links, can potentially be reproduced in global IoV and city traffic control systems [7], but the problem is that stationary trusted nodes are not applicable for irregular routes of a small-scale MAS. Thus, the question arises, if one can design a less expensive route verification scheme without trusted checkpoints and intense human control. Another problem here is that the refusal from trusted nodes and human control in fact means that the level of data storage protection in checkpoints will be reduced substantially, and it is necessary to compensate it somehow. As QKD networks are much more expensive systems than classic ones, they may be equipped with more reliable data storage devices.