State solvability requirements for discrete-valued variables

[henrikt-ma]

According to phone meeting decision on #2639.

To make the section more readable with more variables and equations entering the picture, I've also reordered some variables and equations for a more coherent presentation.

I still wouldn't say that this solves #2639, since there is still no clarification regarding what tools are allowed to do avoid cycles between equations for discrete-valued variables.

[HansOlsson]

Looks good. One minor issue (not new) is that there is an important structure in f_z that we don't include. We could write it as:
0=if "event" then z-pre(z) else f_z(v, c);
or some variation of this, e.g.:
z=f_z(v, c);
with the internal structure:
z_i=if "triggered i" then f_zi(v, c) else pre(z_i);
or even:
z_i=if edge(m_...i) then f_zi(v, c) else pre(z_i)

The reasons to split it like this are:

• Obvious that it is inactive during continuous integration.
• Clear that the number of equations in f_z correspond to the size of z.

[henrikt-ma]

Looks good. One minor issue (not new) is that there is an important structure in f_z that we don't include. We could write it as:
0=if "event" then z-pre(z) else f_z(v, c);
or some variation of this, e.g.:
z=f_z(v, c);
with the internal structure:
z_i=if "triggered i" then f_zi(v, c) else pre(z_i);
or even:
z_i=if edge(m_...i) then f_zi(v, c) else pre(z_i)

The reasons to split it like this are:

• Obvious that it is inactive during continuous integration.
• Clear that the number of equations in f_z correspond to the size of z.

OK, now f_z is only used at events. I'm afraid it would be too much detail to partition z according to how different subsets of equations can be activated by different trigger conditions. I suspect that there are many more details of similar character that we are omitting.

[HansOlsson]

OK, now f_z is only used at events. I'm afraid it would be too much detail to partition z according to how different subsets of equations can be activated by different trigger conditions. I suspect that there are many more details of similar character that we are omitting.

Ok, looks good now.