Rules and initial conditions (2) 

MultiwayPetriNet accepts PetriNetObject expressions:

In[34]:=

Out[34]=

Or lists of places, transitions and arcs:

In[35]:=

Out[35]=

Or associations of places, transitions and arcs:

In[36]:=

Out[36]=

If MultiwayPetriNet is called without an explicit list of token numbers, it is assumed that each place contains no tokens:

In[37]:=

Out[37]=

Event selection functions (2) 

Apply only the first possible event at each step:

In[38]:=

Out[38]=

Apply the first and last possible events at each step:

In[39]:=

Out[39]=

Apply an event selection function for a Petri net specified in list form:

In[40]:=

Out[40]=

Apply an event selection function for a Petri net specified in association form:

In[41]:=

Out[41]=

Specialized Petri net properties (8) 

Construct a Petri net representing a simple producer-consumer problem in concurrency theory:

In[42]:=

Out[42]=

Show the list of Petri net objects obtained after two steps of multiway evolution:

In[43]:=

Out[43]=

Show the list of directed graph representations (with token counts represented graphically) after two steps of multiway evolution:

In[44]:=

Out[44]=

Show the list of directed graph representations (with token counts represented graphically, and with transition firings highlighted) after two steps of multiway evolution:

In[45]:=

Out[45]=

Show the list of directed graph representations (with token counts represented as vertex weights) after two steps of multiway evolution:

In[46]:=

Out[46]=

Show the list of directed graph representations (with token counts represented as vertex weights, and with transition firings highlighted) after two steps of multiway evolution:

In[47]:=

Out[47]=

Show the list of token numbers associated to each place after each firing, following two steps of multiway evolution:

In[48]:=

Out[48]=

Show the list of token numbers associated to each place after each firing (with the corresponding transition firings specified), following two steps of multiway evolution:

In[49]:=

Out[49]=

State node rendering (5) 

By default, states are labeled by their contents:

In[50]:=

Out[50]=

Use no labeling for states:

In[51]:=

Out[51]=

"StatesGraphStructure" yields the same result:

In[52]:=

Out[52]=

Use raw state names as node labels:

In[53]:=

Out[53]=

Use a named shape as each state label:

In[54]:=

Out[54]=

Event node rendering (4) 

By default, both states and events are labeled by their contents:

In[55]:=

Out[55]=

Use no labels for states or events:

In[56]:=

Out[56]=

"EvolutionEventsGraphStructure" yields an equivalent result:

In[57]:=

Out[57]=

Use raw event expressions as their labels:

In[58]:=

Out[58]=

Initialization events (3) 

By default, "AllEventsList" does not include initialization events:

In[59]:=

Out[59]=

The option "IncludeInitializationEvents" allows one to override this default:

In[60]:=

Out[60]=

Initialization events have special default rendering:

In[61]:=

Out[61]=

Graph layout options (2) 

Place arrows in the middle of edges:

In[62]:=

Out[62]=

Generate an example of multiway Petri net evolution:

In[63]:=

Out[63]=

Force a layered digraph embedding:

In[64]:=

Out[64]=

Step numbers and state IDs (5) 

By default, equivalent states are merged across all time steps:

In[65]:=

Out[65]=

In[66]:=

Out[66]=

Merging of equivalent states across different time steps can be prevented by including step numbers:

In[67]:=

Out[67]=

In[68]:=

Out[68]=

Merging of equivalent states at the same time step can be prevented by also including state IDs:

In[69]:=

Out[69]=

In[70]:=

Out[70]=

Step numbers and IDs also apply to events:

In[71]:=

Out[71]=

See the events:

In[72]:=

Out[72]=

State path weights (2) 

Vertices of a states graph can be weighted by their relative rate of occurrence at each time step:

In[73]:=

Out[73]=

Vertices can also be weighted by the number of distinct evolution paths that lead to them:

In[74]:=

Out[74]=

MaxItems (2) 

By default, "CausalGraphInstances" returns all possible causal graphs:

In[75]:=

Out[75]=

The number of causal graphs returned can be limited using MaxItems:

In[76]:=

Out[76]=

Predecessors and resolvents (2) 

By default, "BranchPairsList" returns only a list of branch pairs:

In[77]:=

Out[77]=

Common predecessor states can be shown using "GivePredecessors":

In[78]:=

Out[78]=

Similarly, "BranchPairResolutionsList" by default lists only resolved and unresolved branch pairs:

In[79]:=

Out[79]=

Common resolvents of resolved branch pairs can be shown using "GiveResolvents":

In[80]:=

Out[80]=

Show both common predecessors and common resolvents, where appropriate:

In[81]:=

Out[81]=

Full branchial space (2) 

By default, non-branch pair states are not shown as part of the branchial graph:

In[82]:=

Out[82]=

They can be shown using "IncludeFullBranchialSpace":

In[83]:=

Out[83]=

Graph options (1) 

MultiwayPetriNet supports the same options as Graph:

In[84]:=

Out[84]=

In[85]:=

Out[85]=