# Multiple-Valued Logic Modelling for Agents Controlled via Optical Networks
## 3 Results
### Collective Generation of Data for MVL Storage and Ledger Functions
The accumulated set of user data and random hash values above can be directly used for the formation of the simple version of the logic ledger function, but a more pragmatic variant is to firstly generate the separate backup storage function \(F_{st}\), accessible for distant reconstruction if the prover has declared a correct access key. The simple variant here responds to the reconstruction of entry \(\mathbf{e}_{m}\) when the prover declares (i.e., substitutes as input variables) the collectively generated key given by the hash values \(h_{1}\),..., \(h_{Q}\). The request is sent according to the known list of participants and is considered correct if it is reproduced by the majority of participants. Another simple variant responds to the approval of certificate hash values \(h_{1}\),..., \(h_{q}\) extracted from the storage for the declared entry \(\mathbf{e}_{m}\). Here, the reliability of data also can be estimated according to the majority of replies. More complicated schemes such as the \"proof-of-work\" one in the BC protocol [37, 38, 39] are principally possible, but they seem to be not actual here. If all participants of the collective protocol possess identical data sets \(\{\mathbf{e}_{1},\ldots,\mathbf{e}_{n},\ t,h_{1}\),..., \(h_{q}\}\) written for every entry in the storage, then identical storage function \(F_{st}\) can be generated in all the involved verifiers using the known scheme. Two simple variants of storage function mentioned above are shown further as the function of entries \(F_{st}\) and the function of hash values \(F_{sth}\). As the key to extracting data from backup storage should be realized by hash values \(h_{1}\),..., \(h_{Q}\) assigned by \(Q\) network verifiers, then namely these hash parameters are to be used as input variables in \(F_{st}\). In addition, the set of entries \(\mathbf{e}_{m}\ =\ \{\mathbf{e}_{1,m},\ldots,\mathbf{e}_{n,m}\}\) should be considered as the values of output of the variable \(y\). Such a procedure should use the general algorithm given in [29] and Table 1.  
The formation of the MVL storage function \(F_{sth}\) is shown in Table 2. This truth table follows the general format, so that besides parameters \(h_{1}\),..., \(h_{Q}\) it contains an additional counter of verifier \(q\). For brevity, Table 2 demonstrates the product term only for final entry \(\mathbf{e}_{m}\), and all previously added product terms are not shown. One should especially note that, by default or according to the agreement of participants, the first row in the truth table can be filled in by arbitrarily taken random numbers. If some verifier from the list was switched off and did not take part in the formation of \(F_{entr}\), it is necessary to assign 0 to its hash value in the row. Here, hash values \(h_{1}\),..., \(h_{Q}\) will be the key to the verification procedure, when some of participants will want to restore the entry with critical data. The second version of storage function \(F_{stc}\) can be based on the same data set \(\{e_{1},\ldots,e_{n},\,t,h_{1},\,\ldots,h_{q}\}\) and is shown in Table 3. It is to approve certificate hash values \(h_{1}\),..., \(h_{q}\) for the declared entry \(e_{m}\), i.e., it can output numbers of licenses or permission if entries contain data referring agent and MASs. Actually, this function should reproduce collectively assigned random hash values. A special comment should be given to the assigning of random values to the hash function. Their use is determined by the desire to provide an unpredictability of parameters for the MVL function, the storage function, and the ledger function. As most secured data protection schemes [80] are grounded in the OTP method and random data, AGA verification should also follow this trend, excluding preliminary forecasting of backup functions. The method to assign random hash values in the algorithm described above can use the RO scheme proposed earlier in [77] for the protocol PU.