16-17 May 2019 • Sofia, Bulgaria

Submission: 21 February 2019Notification: 11 March 2019Final Version: 1 April 2019


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Figure 1.
Figure 2.

Places in the generalized nets are the second basic component of its static structure together with the transitions.

Types of GN places

A place can play two roles with respect to a given transition:

  • input place for the transition,
  • output place for the transition.
Example: On Figure 1, place L_1 is input for transition Z and places L_2, L_3 are outputs for this transition.

A place that does not serve as a general input or output place for the whole generalized net, serves both as an output place for one transition and as an input place for another.

Example: On Figure 2, the net's general inputs are places L_1 and L_5 and its general outputs are places L_3 and L_6. Place L_2 is output for transition Z_1 and is input for transition Z_2.

Some places are both input and output places for one transition; i.e. the tokens there can do loop.

Example: On Figure 2, such places are L_4 and L_7.

Places and index matrices

The sets of input and output places of a given transition take part in the construction of its index matrix of predicates. The rows of the index matrix are labeled with the labels of the input places. The columns of the index matrix are labeled with the labels of the output places. The matrix element {IP_i, OP_j} that stays on the intersection of the i-th matrix row and j-th matrix column practically corresponds to the predicate that determines whether a token can pass from the i-th input place and j-th output place of the transition. When constructing the index matrix of a transition, it is important to take into consideration the eventual loops.

Example: Figure 3 represents the index matrix of transition Z_1 from the simple generalized net, given on Figure 2. It is noteworthy that places L_4 and L_7 are input places for the transition Z_1. For the needs of the example, the values of the predicates have been randomly chosen; they do not follow from the graphical structure of the model, but rather from the logic of the modelled process.
  IM =
    L2 L3 L4
L1 false false true
L4 W4,2 false W4,4
L7 W7,2 W7,3 false
Figure 3.