5.1 Fundamentals

The reduction of nets is offered in the main menu under <R> , though only for uncoloured place/transition-nets without time allocation and without use of priorities, because it is only in this case that the reduction steps are appropriate, i.e., that characteristics of the original net can be deduced from the characteristics of the reduced one.

First, the reduction menu, together with the following note, is displayed:

Reduction:
Transitions without pre-places are live and will be deleted together with their
post-places. If such transition has excepted post-places, it will be excepted.
Isolated transitions will be deleted even if they are excepted from reduction!
Reduction menue:
For:                            please, type:
    Quit .......................................Q
    Program a sequence of reduction steps.......P
    change eXceptions...........................X
    connectedness Test..........................T
    save the actual net.........................N
    Raise node numbers with exceptions..........R
    terminal Output of the current net..........O
    reset to the Initial net....................I
    Squeeze the node numbers....................S
    Fusion of congruent nodes...................F
    Merging of equivalent places................M
    ELIMINATION of F(pF)={p}-places.............A
    ELIMINATION of (Fp)F={p}-places.............B
    ELIMINATION of looping places...............C
    DELETION of looping transitions.............U
    DELETION of single output transitions.......V
    DELETION of PTP-sequences...................W
 choice>

For the reduction, you can define exceptions by using the function <X> (see page ), i.e., sets of places and transitions that must not be deleted during reduction.

As INA indicates in the reduction menu, transitions without pre-places are deleted together with their post-places, unless they themselves or one of their post-places are exempted from the reduction. Transitions without pre-places are live, and their post-places are unbounded [Sta90, Regel 1 (85)].

If you reduce a net that contains transitions without pre-places, then these pre-places are not deleted until you use the commands <A> , <B> , <V> or <W> . The search for transitions without pre-places is only performed, if the net was newly read, just set back, or successfully reduced. Please note: Before you start any other reduction procedure, execute one of the specified commands, for the following reason. Should the application of the other procedure be impossible, INA would assume that the net was not changed, and therefore (incorrectly), no search for transitions without pre-places would be performed during the next run-through.

Figure 5.1: A net containing a transition without pre-places (red_simp.pnt)

The simple net of example 5.1 is completely deleted by a single application of one of the preceding commands:

There are transitions without pre-place, the net is not bounded.
 1 live transition(s) deleted
 1 unbounded place(s) deleted
There are transitions without pre-place, the net is not bounded.
 1 live transition(s) deleted
The net is live and totally unbounded.

In the session report, the same situation is described by the following protocol:

deleted (live) transitions:
       1,
deleted (unbounded) places:
       0,
deleted (live) transitions:
       2,
deleted (unbounded) places:
      empty
The net is live and totally unbounded.

In case the current net does not satisfy the conditions of the reduction procedure selected, INA returns to the reduction menu with the message No application possible. With <Q> , you can abort running reductions at any time; steps already begun are finished, and the message Stopped is displayed.

INA records the reduction process on the screen and in the session report. Places and transitions are displayed not with their names, but with their numbers preceded by p or t, respectively.

Isolated nodes which have been created during reduction are always deleted, even if they were exceptions before.

Please note: in the reduced net, the names of places and transitions are often deleted, and values such as capacities and priorities have sometimes not been copied. In case a reduced net is to be analyzed further, it should therefore be checked in the editor beforehand.