The synthesis of a controller which realizes a specified path is described in more detail in [21]. The procedure was developed for a modified version of our Two-Pusher example, and it works as follows:
,so that the token can move through these places from
the initial place to the goal place.
to place 
. This is called a
forward step. Performing a forward step consists of switching on the
necessary control inputs and marking the necessary places which enable
the desired transitions.
, whose
firing would bring the system to an extended forbidden marking.
Then, determine the control inputs which could remove tokens from
other places in 
. That is, ``unlock'' a
situation which would be locked by the safety controller by removing a
token from some other place in before
moving a token to our desired place 
.
There are some limitations of this procedure we must mention: First,
it is purely sequential. This means that the procedure travels through
the desired sequence, step by step, as opposed to devising perhaps
certain strategies which would guarantee the accomplishment of the
desired path. Second, if we find a controller with this procedure,
then this controller is suitable; but, there is no guarantee that we
will find a controller if one exists, or that the one we find is
``optimal'' in any sense. These problems are currently under
investigation.
From the results of the above procedure, we can directly derive the
controller function and represent it by means of a Sequential Function
Chart which can be directly implemented in a Programmable Logic
Controller (PLC). Synthesizing the control code automatically from
the results of the above algorithm is described in [7].
We will illustrate this procedure for the desired path specification
of the Two-Pusher example in Section 6.4.