System Types (5) 

CausalInvariantQ supports both string and list substitution systems:

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Lists can contain arbitrary symbolic elements:

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Give an explicit substitution system rule:

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An alternative method of specifying that a substitution system should be used:

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CausalInvariantQ also supports multiway generalizations of cellular automata:

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CausalInvariantQ also supports multiway generalizations of Wolfram Models:

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Construct a multiway evolution by explicitly specifying an association:

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Rules and Initial Conditions (2) 

CausalInvariantQ accepts both individual rules and lists of rules:

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Likewise for initial conditions:

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Event Selection Functions (3) 

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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Use a greedy-style algorithm to apply the maximal set of non-conflicting events at each step (strings only):

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Step Numbers and State IDs (3) 

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

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Causal Invariant Rules (2) 

Prove that the Xor and And functions are causal invariant (due to associativity):

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On the other hand, the Nand function is not associative, so it is not causal invariant:

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