Improve sm (modelica#2735)

* Clarify the merging of connections to multiple outputs.
1. It doesn't make sense to require them to connected to one "input", it makes more sense that they combine as one "source".
2. The merging according to previous section doesn't make sense as an explanation:
* The "v" variable is one and not one per state so it doesn't apply.
* The "v" is not even an "outer output".
* And finally I don't see how the first variant simplifies anything.
* The intermediate algorithm will require a start-value even if we are always in one of the states.
* The extra code is an algorithm, and we generally try to avoid that.
3.  List the exception also for connections.

Co-authored-by: Henrik Tidefelt <henrikt@wolfram.com>

chapters/connectors.tex

@@ -591,7 +591,7 @@ \section{Restrictions of Connections and Connectors}\label{restrictions-of-conne
   The matched primitive components of the two connectors must have the same primitive types, and flow variables may only connect to other flow variables, stream variables only to other stream variables, and causal variables (\lstinline!input!/\lstinline!output!) only to causal variables (\lstinline!input!/\lstinline!output!).
 \item
   A connection set of causal variables (\lstinline!input!/\lstinline!output!) may at most
-  contain variables from one inside \lstinline!output! connector or one public
+  contain variables from one inside \lstinline!output! connector (for state-machines extended as specified in \cref{merging-connections-to-multiple-outputs}) or one public
   outside \lstinline!input! connector.
   \begin{nonnormative}
   I.e., a connection set may at most contain one source of a signal.

chapters/statemachines.tex

@@ -358,7 +358,7 @@ \subsection{Reset Handling}\label{reset-handling}
 
 \subsection{Activation handling}\label{activation-handling}
 
-When a state is suspended its equations should not be executed, and its variables keep their value -- including state-variables in clocked discretized continuous-time equations.
+When a state is suspended its equations should not be executed, and its variables keep their values -- including state-variables in clocked discretized continuous-time equations.
 
 The execution of a sub-state machine has to be suspended when its
 enclosing state is not active. This activation flag is given as a
@@ -428,35 +428,24 @@ \subsection{Merging Variable Definitions}\label{merging-variable-definitions}
 \subsection{Merging Connections to Multiple Outputs}\label{merging-connections-to-multiple-outputs}
 
 \begin{nonnormative}
-Since instances of blocks can be used as states of a state
-machine it is natural to extend the connection semantics of Modelica to
-allow several outputs to be connected to one input.
+The causal connection semantics of Modelica for non-state machines are generalized to states of state machines, using the fact that only one state is active at a time.
 \end{nonnormative}
 
-It is possible to connect several outputs to an input if all the outputs
-come from states of the same state machine. In such cases, we get the
-following constraint equations:
+It is possible to connect outputs each coming from different states of state machines together -- and connect this with other causal connectors.
+These outputs are combined seen as one source of the signal, and give the following constraint equations,
 \begin{lstlisting}[language=modelica,escapechar=!]
 u!\textsubscript{1}! = u!\textsubscript{2}! = ... = y!\textsubscript{1}! = y!\textsubscript{2}! = ...
 \end{lstlisting}
-with u\textsubscript{i} inputs and y\textsubscript{i} outputs. The
-semantics is defined as follows. Introduce a variable v representing the
-signal flow and rewrite the equation above as a set of equations for
-u\textsubscript{i} and a set of assignment equations for v:
+with \lstinline!y!\textsubscript{i} being outputs from different states of the state-machine and \lstinline!u!\textsubscript{i} being other causal variables.
+The semantics is defined similarly to \cref{merging-variable-definitions}:
 \begin{lstlisting}[language=modelica,escapechar=!]
-v := if activeState(state!\textsubscript{1}!) then y!\textsubscript{1}! else last(v);
-v := if activeState(state!\textsubscript{2}!) then y!\textsubscript{2}! else last(v);
-...
-u!\textsubscript{1}! = v
-u!\textsubscript{2}! = v
-...
-\end{lstlisting}
-
-The merge of the definitions of v is then made according to \cref{merging-variable-definitions}:
-Merging Variable Definitions. The result is after
-simplification:
-\begin{lstlisting}[language=modelica,escapechar=!]
-v := if activeState(state!\textsubscript{1}!) then y!\textsubscript{1}! elseif activeState(state!\textsubscript{2}!) then y!\textsubscript{2}! elseif ... else last(v);
+v = if activeState(state!\textsubscript{1}!) then
+      y!\textsubscript{1}!
+    elseif activeState(state!\textsubscript{2}!) then
+      y!\textsubscript{2}!
+    elseif $\ldots$
+    else
+      last(v);
 u!\textsubscript{1}! = v
 u!\textsubscript{2}! = v
 ...