# Multiple-Valued Logic Modelling for Agents Controlled via Optical Networks
## 3 Results
### Collective Generation of Data for MVL Storage and Ledger Functions  
In Figure 4, the simple procedure is proposed to accumulate data collectively, which is necessary for the generation of an MVL logic-linked list and ledger functions. The prover \(P\) is considered as the participant of the pool of loyal nodes. The prover agent wants to add some entry \(e\ =\ \{e_{1},\ldots,e_{n}\}\) into the distributed backup storage, which is being sustained collectively by the pool of network nodes. We suppose that this entry is not confidential and does not need preliminary secret coding, but even this procedure will not disturb the procedures disclosed further. The prover \(P\) has the list \(N_{N}\ =\ \big{\{}N_{1},\ldots,\ N_{Q}\big{\}}\) of identifiers (or simply numbers \(1,\ldots,Q\)) corresponding to verifiers \(V_{1},V_{2},\ldots,V_{Q}\), who are agreed to provide the service. Principally, some of the participants can be switched off or busy, so that full list can be unused, but this does not change the scheme, and for simplicity we  
Figure 3: (**a**) The basic scheme to calculate function in AGA. (**b**) The simple scheme to use additional counter \(x_{N_{0}+1}\) in order to receive \(k-1\) output values for the same set of input vectors given for MVL function. suppose that all registered participants are taking part in the formation of the entry. The prover \(P\) tags the entry \(\mathbf{e}\ =\ \{e_{1}\,\ldots,e_{n}\}\) as a new one and sends it via the network to one of the participants, which is taken to be \(V_{1}\). Verifier \(V_{1}\) assigns to this entry the time stamp \(t\) and some randomly chosen natural number \(h_{1}\). After this, \(V_{1}\) writes the set of parameters \(\{e,\ t,\ h_{1}\}\) in its memory and sends the copy back to the prover. Further, prover \(P\) writes the obtained parameters in memory and sequentially sends the pair \(\{e,\ t\}\) to all other nodes from the list. As a result, it accumulates random hash function values \(h_{1},\ldots,h_{Q}\) assigned by verifiers \(V_{1},V_{2},\ldots,V_{Q}\) to the pair \(\{e,\ t\}\). After this, \(P\) sends the finally formed set \(\{e_{1},\ldots,e_{n},\ t,h_{1}\,\ldots,h_{Q}\}\) to all involved participants according to the earlier used list. Further, this set of data is to be represented as a separate logic product term in the collective ledger function. The procedure given above is shown further as Algorithm 1. Its necessary preliminary conditions for entry formation include:  
* complete number of involved loyal verifiers \(Q\) should respond to \(Q\leq k-1\);
* waiting time \(t_{wait}\) is limited for the reply from the verifier \(V_{j+1}\). If it is exceeded, then the zero value should be assigned to the corresponding \(h_{j+1}\);
* every node taking part in the protocol should possess either quantum random number generator or RO module with the scheme proposed in [77], which should generate the set of randomly given hash values \(h_{j}\) to make the formation of entries unpredictable and corresponding product terms;
* all the assigned parameters are natural numbers. Figure 4: The scheme of assigning random hash values \(h\) by verifiers to the entry received from the mobile agent P.  
As the prover sends its entry \(\mathbf{e}\) according to the preliminary formed list of participants, the number of replies does not exceed \(Q\). As the limiting time parameter \(t_{wait}\) is assigned in the reply only by the first verifier, its possible further illegal modification in one of verifiers does not influence the other's replies and will contradict the data of the simple majority of verifiers and will be excluded at the stage of decision making. The absence of the verifier's reply is marked by a zero hash, which is fixed in all other procedures and can be further used for analysis of attacks. The waiting time \(t_{wait}\) period for reply can be limited by the average and variance values estimated for all involved verifiers.