
diff -r c7825cfacc76 -r cc12352272f2 etnms/etnms.tex
--- a/etnms/etnms.tex	Wed Feb 05 11:54:51 2020 +0000
+++ b/etnms/etnms.tex	Wed Feb 05 12:01:57 2020 +0000
@@ -561,15 +561,16 @@
 					       & &$\phantom{\textit{then},\;_{bs}\oplus\,}(\textit{fuse}\,(\textit{bmkeps}\,a_1)\,(a_2\,\backslash c))]$\\
   & &$\textit{else}\;_{bs}\,(a_1\,\backslash c)\cdot a_2$\\
   $(_{bs}a^*)\,\backslash c$ & $\dn$ &
-      $_{bs}\;((\textit{fuse}\, [0] (r\,\backslash c))\cdot
+      $_{bs}(\textit{fuse}\, [0] \; r\,\backslash c)\cdot
        (_{[]}r^*))$
 \end{tabular}    
 \end{center}    
 
 %\end{definition}
 \noindent
-For instance, when we unfold $_{bs}a^*$ into a sequence,
-we need to attach an additional bit $0$ to the front of $r \backslash c$
+For instance, when we do derivative of  $_{bs}a^*$ with respect to c,
+we need to unfold it into a sequence,
+and attach an additional bit $0$ to the front of $r \backslash c$
 to indicate that there is one more star iteration. Also the sequence clause
 is more subtle---when $a_1$ is $\textit{bnullable}$ (here
 \textit{bnullable} is exactly the same as $\textit{nullable}$, except
@@ -593,15 +594,15 @@
 %\begin{definition}[\textit{bmkeps}]\mbox{}
 \begin{center}
 \begin{tabular}{lcl}
-  $\textit{bmkeps}\,(\textit{ONE}\;bs)$ & $\dn$ & $bs$\\
-  $\textit{bmkeps}\,(\textit{ALTS}\;bs\,a::as)$ & $\dn$ &
+  $\textit{bmkeps}\,(_{bs}\ONE)$ & $\dn$ & $bs$\\
+  $\textit{bmkeps}\,(_{bs}\oplus a::\textit{as})$ & $\dn$ &
      $\textit{if}\;\textit{bnullable}\,a$\\
   & &$\textit{then}\;bs\,@\,\textit{bmkeps}\,a$\\
-  & &$\textit{else}\;bs\,@\,\textit{bmkeps}\,(\textit{ALTS}\;bs\,as)$\\
-  $\textit{bmkeps}\,(\textit{SEQ}\;bs\,a_1\,a_2)$ & $\dn$ &
+  & &$\textit{else}\;bs\,@\,\textit{bmkeps}\,(_{bs}\textit{as})$\\
+  $\textit{bmkeps}\,(_{bs} a_1 \cdota_2)$ & $\dn$ &
      $bs \,@\,\textit{bmkeps}\,a_1\,@\, \textit{bmkeps}\,a_2$\\
-  $\textit{bmkeps}\,(\textit{STAR}\;bs\,a)$ & $\dn$ &
-     $bs \,@\, [\S]$
+  $\textit{bmkeps}\,(_{bs}a^*)$ & $\dn$ &
+     $bs \,@\, [1]$
 \end{tabular}    
 \end{center}    
 %\end{definition}




