Code
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Results

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MultiwayOperatorSystem[{And[a_,b_]And[b,a],Or[a_,b_]Or[b,a],And[a_,Or[b_,Not[b_]]]a,Or[a_,And[b_,Not[b_]]]a,a_Module[{b=Unique[]},And[a,Or[b,Not[b]]]],a_Module[{b=Unique[]},Or[a,And[b,Not[b]]]],And[a_,Or[b_,c_]]Or[And[a,b],And[a,c]],Or[And[a_,b_],And[a_,c_]]And[a,Or[b,c]],Or[a_,And[b_,c_]]And[Or[a,b],Or[a,c]],And[Or[a_,b_],Or[a_,c_]]Or[a,And[b,c]]},{And[a,b]},1,"StatesGraph"]
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MultiwayOperatorSystem[{And[a_,b_]And[b,a],Or[a_,b_]Or[b,a],And[a_,Or[b_,Not[b_]]]a,Or[a_,And[b_,Not[b_]]]a,a_Module[{b=Unique[]},And[a,Or[b,Not[b]]]],a_Module[{b=Unique[]},Or[a,And[b,Not[b]]]],And[a_,Or[b_,c_]]Or[And[a,b],And[a,c]],Or[And[a_,b_],And[a_,c_]]And[a,Or[b,c]],Or[a_,And[b_,c_]]And[Or[a,b],Or[a,c]],And[Or[a_,b_],Or[a_,c_]]Or[a,And[b,c]]},{And[a,b]},3,"StatesGraphStructure"]
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"A#B""#AB#"
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MultiwayOperatorSystem[{CircleDot[a_,CircleDot[b_,c_]]CircleDot[CircleDot[a,b],c],CircleDot[CircleDot[a_,b_],c_]CircleDot[a,CircleDot[b,c]],CircleDot[a,CircleDot[x_,b]]CircleDot[x,CircleDot[a,CircleDot[b,x]]]},{CircleDot[a,CircleDot[CircleDot[x,y],b]]},3,"StatesGraph"]
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MultiwayOperatorSystem[{Equal[a_,b_]Equal[b,a],CircleDot[a_,CircleDot[b_,c_]]CircleDot[CircleDot[a,b],c],CircleDot[CircleDot[a_,b_],c_]CircleDot[a,CircleDot[b,c]],aCircleDot[a,b]},{CircleDot[a,a]CircleDot[a,CircleDot[CircleDot[a,b],b]]},1,"StatesGraph"]
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MultiwayOperatorSystem[{Equal[a_,b_]Equal[b,a],CircleDot[a_,CircleDot[b_,c_]]CircleDot[CircleDot[a,b],c],CircleDot[CircleDot[a_,b_],c_]CircleDot[a,CircleDot[b,c]],aCircleDot[a,b]},{CircleDot[a,a]CircleDot[a,CircleDot[CircleDot[a,b],b]]},2,"StatesGraph"]
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Boolean algebra