# Multiple-Valued Logic Modelling for Agents Controlled via Optical Networks
## 1 Introduction
### Mobile Robotic Agents and Position-Based Cryptography Schemes  
Hardware mobile robotic agents are now represented by autonomous vehicles [7; 69], collectives of agents [70], and industrial [8] and healthcare systems [9]. The review of applications for wireless sensor networks formed by mobile agents was presented in [71] and included such tasks as required data collection from the field of view by drones, traffic control, biomedical health and environmental monitoring, virtual reality, and industrial systems control, as well as target tracking, urban control, monitoring of events, and intrusion detection. Another trend here is the research of schemes for position control and verification of mobile agents [72], where quantum optics is involved as the tool to raise the security level. A position-based cryptography (PBC) task [22] is the confidential transmission of messages from one space location to another one, excluding the decoding of this message by any receiver having any other space coordinates. This task dates back to an ongoing problem of position verification of subscribers in mobile telephony [73], which has caused attempts to use QKD and to obtain unconditional security to not depend on the computing resources of the eavesdropper. The most secured quantum PBC protocol was proven theoretically by [PERSON] [33] and is further tagged as PU. In fact, this protocol tried to prevent an actual \"man-in-the-middle\" attack [74] for the quantum optics scheme, but it has obtained only a partial result and did not provide unconditional security for the PBC scheme, as it can be deceived by a large enough number of fake qubits randomly emitted by illegal laser sources located between the eavesdropper and verifiers. This protocol [33] involves quite a realistic laser atmospheric QKD line with an Einstein-Podolsky-Rosen (EPR) source of entangled photon pairs [75]. However, in the review [22] protocol, PU was estimated as an interesting but purely theoretical scheme, as it involves an ideal random oracle (RO), which principally cannot be obtained in practice. RO here is the ideal black box, which for an arbitrary input signal generates random outputs with a fixed number of bits [76]. The obligatory conditions for RO are that it should reproduce the output for any repeated input, and there should be no ways to predict its output. In order to use protocol PU in practice, the scheme for an RO device was proposed in the paper [77] and included a memory device learned by a quantum random number generator [78] with the help of a special algorithm. Such a scheme of an RO device was intended for the verification of a planned route for passing by a mobile autonomous vehicle [79]. This verification scheme is being discussed further, together with the verification scheme from [77], so that both of them are schematically shown in Figure 2.  
The task of a verification procedure is to check the prehistory of visits of a mobile agent to checkpoints. According to terms used in [33], the mobile agent \(P\) within the verification scheme is regarded as a prover requesting some service and initially approving its space position for this. The idea of protocol PU [33] was discussed in [32,77] for a 2D case. At every checkpoint, agent \(P\) passes through the special quantum optics scheme, shown in Figure 2, by \"crossed\" pairs of verifier modules. Every such \"cross\" scheme of a verifier is supposed to emit and detect qubits (i.e., quantum bits or single photons characterized by some quantum states \(|\,\Psi\!\!>\)) and is also supposed to exchange classical laser signals with the prover. The protocol is activated when the prover \(P\) sends the initial request signal. The verifier replies by subsequent transfer of random classical data \(x_{1},x_{2}\) and qubit \(|\,\Psi\!\!>\). (As there is yet no appropriate quantum memory for qubit storage, it is necessary to transfer it with some time delay after classical ones.)