## 4 Experiment Evaluations  
In this section, two groups of experiments were carried out. The first group of experiments was to evaluate the effectiveness of RMO_SODSDDA, and the second was to evaluate its efficiency. All experiments were implemented on a standard desktop PC with an Intel i5-7400 CPU, 4 GB RAM, and 160 GB hard disks, running a 64-bit Windows 7 operating system. All simulations were compiled and executed in Eclipse IDE for a Java Developers environment.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Permissions Request** & **HC** & \(SC\) \\ \hline \(<\)\(s\),\(\Phi\),\(\{p_{2},p_{3},p_{6}\}\),\(max>\) & \(HC\cup\{\
eg\bar{p}_{0},\
eg\bar{p}_{1},\
eg\bar{p}_{4},\
eg\bar{p}_{5},\
eg\bar{p}_{7}\}\) & \(\{\bar{p}_{2},\bar{p}_{3},\bar{p}_{6}\}\) \\ \hline \(<\)\(s\),\(\{p_{2},p_{3},p_{6}\}\),\(P\),\(min>\) & \(HC\cup\{\bar{p}_{2},\bar{p}_{3},\bar{p}_{6}\}\) & \(\{\
eg\bar{p}_{0},\
eg\bar{p}_{1},\
eg\bar{p}_{4},\
eg\bar{p}_{5},\
eg\bar{p}_{7}\}\) \\ \hline \(<\)\(s\),\(\{p_{2},p_{3},p_{6}\}\),\(\{p_{2},p_{3},p_{6}\}\),\(exact>\) & \(HC\cup\{\bar{p}_{2},\bar{p}_{3},\bar{p}_{6}\}\) & \(\Phi\) \\ \(\bar{p}_{6},\
eg\bar{p}_{0},\
eg\bar{p}_{1},\
eg\bar{p}_{4},\
eg\bar{p}_{5}, \
eg\bar{p}_{7}\}\) & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Updated clauses.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Authorization Logics and Constraints** & **HC** \\ \hline \(\forall p\in P,\exists(r,r^{\prime})\in\mathrm{R}:\) & \(\
eg\bar{r}_{0}\lor p_{0},\
eg\bar{r}_{0}\lor\bar{p}_{1},\
eg\bar{r}_{0}\lor p _{2},\
eg\bar{r}_{0}\lor\bar{p}_{4}\), \\ \(((r,r^{\prime})\in\mathrm{RH})\wedge((p,r^{\prime})\in\mathrm{PA})\) & \(\
eg\bar{r}_{0}\lor\bar{p}_{5},\
eg\bar{r}_{0}\lor\bar{p}_{6},\
eg\bar{r}_{1} \lor\bar{p}_{3},\
eg\bar{r}_{1}\lor\bar{p}_{7}\), \\  & \(\
eg\bar{r}_{2}\lor\bar{p}_{2},\
eg\bar{r}_{2}\lor\bar{p}_{6}\) \\ \hline \(\forall p\in P,\exists(r^{\prime},r_{1},r_{2},\ldots)\in\mathrm{R}:\) & \(\
eg\bar{p}_{0}\lor\bar{r}_{0},\
eg\bar{p}_{1}\lor\bar{r}_{0},\
eg\bar{p}_{2} \lor\bar{r}_{0}\lor\bar{r}_{2},\
eg\bar{p}_{3}\lor\bar{r}_{1}\), \\ \(((p,r^{\prime})\in\mathrm{PA})\wedge((r_{1},r^{\prime})\in\mathrm{RH})\wedge((r_{2}, r^{\prime})\in\mathrm{RH})\) & \(\
eg\bar{p}_{4}\lor\bar{r}_{0},\
eg\bar{p}_{5}\lor\bar{r}_{0},\
eg\bar{p}_{6} \lor\bar{r}_{0}\lor\bar{r}_{2},\
eg\bar{p}_{7}\lor\bar{r}_{1}\) \\ \hline \(\forall r\in R,\exists r^{\prime}\in\mathrm{R},\exists(p_{1},p_{2},\ldots)\in \mathrm{P}:\) & \(\
eg\bar{r}_{0}\lor\bar{r}_{0}\lor\
eg\bar{p}_{1}\lor\bar{r}_{0},\
eg\bar{p}_{2} \lor\bar{r}_{0}\lor\bar{r}_{2},\
eg\bar{p}_{3}\lor\bar{r}_{1}\) \\ \(((r,r^{\prime})\in\mathrm{RH})\wedge((p_{1},r^{\prime})\in\mathrm{PA})\wedge((p_{2}, r^{\prime})\in\mathrm{PA})\) & \(\
eg\bar{r}_{0}\lor\bar{r}_{0},\
eg\bar{p}_{5}\lor\bar{r}_{0},\
eg\bar{p}_{6} \lor\bar{r}_{0}\lor\bar{r}_{2},\
eg\bar{p}_{7}\lor\bar{r}_{1}\) \\ \hline \(\forall r\in R,\exists r^{\prime}\in\mathrm{R},\exists(p_{1},p_{2},\ldots)\in \mathrm{P}:\) & \(\
eg\bar{r}_{0}\lor\
eg\bar{p}_{1}\lor\
eg\bar{p}_{2}\lor\bar{r}_{4}\lor\
eg \bar{p}_{5}\lor\
eg\bar{p}_{6}\) \\ \(((r,r^{\prime})\in\mathrm{RH})\wedge((p_{1},r^{\prime})\in\mathrm{PA})\wedge((p_{2}, r^{\prime})\in\mathrm{PA})\) & \(\
eg\bar{r}_{1}\lor\
eg\bar{p}_{3}\lor\
eg\bar{p}_{7},\bar{r}_{2}\lor\
eg\bar{p}_{2} \lor\
eg\bar{p}_{6}\) \\ \hline \(\forall s\in S,\ \exists[r_{1},r_{2},\ldots]\in\mathrm{R}:\) & \(\
eg\bar{r}_{0}\lor\
eg\bar{r}_{1}\) \\ \(\mathrm{dmer}(\{r_{1},r_{2},\ldots],2,s\}\in\mathrm{C}\) & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Hard clauses.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Permissions Request** & **HC** & **SC** \\ \hline \(<\)\(s\),\(\Phi\),\(\{p_{2},p_{3},p_{6}\}\),\(max>\) & \(HC\cup\{\
eg\bar{p}_{0},\
eg\bar{p}_{1},\
eg\bar{p}_{4},\
eg\
eg\bar{p}_{5},\
eg\bar{p}_{7}\}\) & \(\{\bar{p}_{2},\bar{p}_{3},\bar{p}_{6}\}\) \\ \hline \(<\)\(s\),\(\{p_{2},p_{