Resolution:
## Figure 5.
Implicit representation of extended Petri nets by controled reactions. A controled reaction is composed of the reaction vector R= (r,_{c }f_{r}) r and the associated control function . The arcs of an extended Petri net can be thought of to consist of two sets. (1)
The standard arcs and (2) the control arcs (bidirected arcs and inhibitory arcs).
A reaction vector describes how the marking of the connected places changes upon firing
of a transition. The control function defines the conditions under which firing of
at least one of all transitions with the same reaction vector may occur. The marking
of the places of all four Petri nets shown in panels a) to d) has been choosen such
that all transitions can fire. If there is a token in place A, the transition in a)
can always fire, the transition in b) can only fire if there is at least one token
in place C, while the transition in c) can only fire if there is at least one token
in place C and if place D is empty. In the Petri net of panel d), the token has two
options to move from place A to place B. It can move through firing of f_{r}T_{1 }if there is at least one token in place C and at least one token in place D. The alternative
path, firing of T_{2}, requires that there is at least one token in place D while place E must be empty.
In panel d), the reaction vector of the controled reaction represents the set of two transitions R= (r,_{c }f_{r}) T_{1 }and T_{2 }each of which connects the places A and B in the same direction through standard arcs.
Note that if places A in panels a) to d) do not contain any token, none of the transitions
could fire. Symbols: ∧, logic AND; ∨, logic OR; -, logic NOT.
Durzinsky |