## 7 The TFL-Free Property
### Algorithm for TFL-Free SDN Updating
#### 7.2.1 Algorithm Overview
\begin{table}
\begin{tabular}{c c} \hline \hline
**Message** & \(CI_{\mathbf{rp}}\) \\ \hline \multicolumn{3}{c}{Control information of delete messages that correspond to \(match_{1}\)} \\ \(m_{1}\) & \([(cp,1)]\) \\ \(m_{2}\) & \([(cp,1),(cp,2)]\) \\ \(m_{3}\) & \([(cp,1),(cp,2),(cp,3)]\) \\ \(-\) & \([(cp,1),(cp,2),(cp,3),\ldots,(cp,n-2)]\) \\ \(m_{n-1}\) & \([(cp,1),(cp,2),(cp,3),\ldots,(cp,n-2),(cp,n-1)]\) \\ \(m_{n}\) & \([(cp,1),(cp,2),(cp,3),\ldots,(cp,n-2),(cp,n-1),(cp,n)]\) \\ \multicolumn{3}{c}{Control information of delete messages that correspond to \(match_{2}\)} \\ \(m_{n+1}\) & \([(cp,n+1)]\) \\ \(m_{n+2}\) & \([(cp,n+1),(cp,n+2)]\) \\ \(m_{n+3}\) & \([(cp,n+1),(cp,n+2),(cp,n+3)]\) \\ \(-\) & \(-\) \\ \(m_{n+m}\) & \([(cp,n+1),(cp,n+2),(cp,n+3),(cp,n+4),\ldots,(cp,n+m)]\) \\ \(m_{n+m+1}\) & \([(cp,n+1),(cp,n+2),(cp,n+3),(cp,n+4),\ldots,(cp,n+m),(cp,n+m+1)]\) \\ \multicolumn{3}{c}{Control information of add messages that correspond to \(match_{1}\)} \\ \(m_{n+m+2}\) & \([Cl_{\text{rp}}\) of \(m_{n}+(cp,n+m+2)]\) \\ \(m_{n+m+3}\) & \([Cl_{\text{rp}}\) of \(m_{n}+(cp,n+m+2),(cp,n+m+3)]\) \\ \(m_{n+m+4}\) & \([Cl_{\text{rp}}\) of \(m_{n}+(cp,n+m+2),(cp,n+m+3),(cp,n+m+4)]\) \\ \(-\) & \(-\) \\ \(-\) & \(-\) \\ \(m_{n+m+k+j}\) & \([Cl_{\text{rp}}\) of \(m_{n}+(cp,n+m+2),(cp,n+m+3),(cp,n+m+5),\ldots,(cp,n+m+k),(cp,n+m+k+1)]\) \\ \multicolumn{3}{c}{Control information of add messages that correspond to \(match_{2}\)} \\ \(m_{n+m+k+2}\) & \([Cl_{\text{rp}}\) of \(m_{n+m+1}+(cp,n+m+k+2)]\) \\ \(m_{n+m+k+3}\) & \([Cl_{\text{rp}}\) of \(m_{n+m+1}+(cp,n+m+k+2),(cp,n+m+k+2)]\) \\ \(m_{n+m+k+4}\) & \([Cl_{\text{rp}}\) of \(m_{n+m+1}+(cp,n+m+k+2),(cp,n+m+k+3),(cp,n+m+k+4)]\) \\ \(-\) & \(-\) \\ \(-\) & \(-\) \\ \(m

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