Generators, Relations, Identity and Inverses (1) 

MultiwayGroup accepts both partial and full (association) specifications of groups in terms of generators, relations, identity element and inverse elements:

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Commutativity (1) 

MultiwayGroup can handle both abelian and non-abelian (default) groups:

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Event Selection Functions (2) 

Apply only the first possible event at each step:

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Apply the first and last possible events at each step:

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Commutativity (2) 

By default, all groups are non-abelian:

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Make the group abelian:

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Append Only (2) 

By default, MultiwayGroup evolves by applying generators at all possible places within a word:

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Apply generators only at the end of the word:

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Edge Styling (2) 

By default, edges are styled in red if they correspond to the application of a generator, green if they correspond to the application of a relation, cyan if they correspond to the application of the identity element, magenta if they correspond to the application of an inverse element and blue if they correspond to the application of commutativity:

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Use no styling for edges:

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State Node Rendering (5) 

By default, states are labeled by their contents:

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Use no labeling for states:

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"StatesGraphStructure" yields the same result:

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Use raw state names as node labels:

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Use a named shape as each state label:

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Event Node Rendering (4) 

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

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Use no labels for states or events:

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"EvolutionEventsGraphStructure" yields an equivalent result:

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Use raw event expressions as their labels:

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Initialization Events (2) 

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

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

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Initialization events have special default rendering:

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Graph Layout Options (2) 

Place arrows in the middle of edges:

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Generate an example of a (free) multiway group:

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Force the initial state nodes to be at the top:

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Step Numbers and State IDs (2) 

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

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

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List the states:

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

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List the states:

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Step numbers and state IDs also apply to events:

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See the events:

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Event Instances (2) 

By default, multiple instances of equivalent updating events are merged in the states graph:

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Merging of equivalent events can be prevented by including event instances:

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State (Path) Weights (2) 

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

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

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MaxItems (2) 

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

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The number of causal graphs can be limited using MaxItems:

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Predecessors and Resolvents (2) 

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

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Common predecessor states can be shown using "GivePredecessors":

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

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

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Show both common predecessors and common resolvents, where appropriate:

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Full Branchial Space (2) 

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

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They can be shown using "IncludeFullBranchialSpace":

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