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ResourceFunction["StringTuples"]["AB",4]
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{AAAA,AAAB,AABA,AABB,ABAA,ABAB,ABBA,ABBB,BAAA,BAAB,BABA,BABB,BBAA,BBAB,BBBA,BBBB}
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ResourceFunction["MultiwaySystem"][{"AB"->"BA","BA"->"AB"},ResourceFunction["StringTuples"]["AB",4],5,"StatesGraph"]
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ResourceFunction["MultiwaySystem"][{"AB"->"BA","BA"->"AB"},ResourceFunction["StringTuples"]["AB",4],5,"CausalGraph"]
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SimpleGraph[ResourceFunction["MultiwaySystem"][{"AB"->"BA","BA"->"AB"},ResourceFunction["StringTuples"]["AB",4],5,"CausalGraph"]]
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ResourceFunction["MultiwaySystem"][{"AB"->"BA","BA"->"AB"},"ABBA",4,"StatesGraph"]
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SimpleGraph[ResourceFunction["MultiwaySystem"][{"AB"->"BA","BA"->"AB"},ResourceFunction["StringTuples"]["AB",2],5,"CausalGraph"]]
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SimpleGraph[ResourceFunction["MultiwaySystem"][{"AB"->"BA","BA"->"AB"},ResourceFunction["StringTuples"]["AB",3],5,"CausalGraph"]]
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SimpleGraph[ResourceFunction["MultiwaySystem"][{"AB"->"BA","BA"->"AB"},ResourceFunction["StringTuples"]["AB",4],5,"CausalGraph"]]
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SimpleGraph[ResourceFunction["MultiwaySystem"][{"AB"->"BA","BA"->"AB"},ResourceFunction["StringTuples"]["AB",2],5,"EvolutionCausalGraph"]]
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Path counting
Path counting
How many ways are there to get from this configuration to that? Without deduplication, there might easily be an infinite number. After deduplication, these become loops.