DAG: Symmetric closure of transitive closure vs. transitive closure of symmetric closure
Am I right in deducing that if I apply first the transitive closure tran() on a directed acyclic graph and then the symmetric closure sym(), the result is different than if I first apply the symmetric closure and then the transitive closure. In the latter case, the reflexive closure is also computed (indirectly).
sym(tran(dag)) != tran(sym(dag))
A-->B-->C : (A,B),(B,C) =tran=> (A,B),(B,C),(A,C) =sym=> (A,B),(B,A),(B,C),(C,B),(A,C),(C,A)
A-->B-->C : (A,B),(B,C) =sym=> (A,B),(B,A),(B,C),(C,B) =tran=> (A,B),(B,A),(A,A),(B,C),(C,B),(B,B),(A,C),(C,A),(C,C)
closures directed-acyclic-graphs associativity symmetric transitive-closure
asked Nov 12 '18 at 12:54
Radio ControlledRadio Controlled
19010
add a comment |
Am I right in deducing that if I apply first the transitive closure tran() on a directed acyclic graph and then the symmetric closure sym(), the result is different than if I first apply the symmetric closure and then the transitive closure. In the latter case, the reflexive closure is also computed (indirectly).
sym(tran(dag)) != tran(sym(dag))
A-->B-->C : (A,B),(B,C) =tran=> (A,B),(B,C),(A,C) =sym=> (A,B),(B,A),(B,C),(C,B),(A,C),(C,A)
A-->B-->C : (A,B),(B,C) =sym=> (A,B),(B,A),(B,C),(C,B) =tran=> (A,B),(B,A),(A,A),(B,C),(C,B),(B,B),(A,C),(C,A),(C,C)
closures directed-acyclic-graphs associativity symmetric transitive-closure
asked Nov 12 '18 at 12:54
Radio ControlledRadio Controlled
19010
add a comment |
Am I right in deducing that if I apply first the transitive closure tran() on a directed acyclic graph and then the symmetric closure sym(), the result is different than if I first apply the symmetric closure and then the transitive closure. In the latter case, the reflexive closure is also computed (indirectly).
sym(tran(dag)) != tran(sym(dag))
A-->B-->C : (A,B),(B,C) =tran=> (A,B),(B,C),(A,C) =sym=> (A,B),(B,A),(B,C),(C,B),(A,C),(C,A)
A-->B-->C : (A,B),(B,C) =sym=> (A,B),(B,A),(B,C),(C,B) =tran=> (A,B),(B,A),(A,A),(B,C),(C,B),(B,B),(A,C),(C,A),(C,C)
closures directed-acyclic-graphs associativity symmetric transitive-closure
asked Nov 12 '18 at 12:54
Radio ControlledRadio Controlled
19010
Am I right in deducing that if I apply first the transitive closure tran() on a directed acyclic graph and then the symmetric closure sym(), the result is different than if I first apply the symmetric closure and then the transitive closure. In the latter case, the reflexive closure is also computed (indirectly).
sym(tran(dag)) != tran(sym(dag))
A-->B-->C : (A,B),(B,C) =tran=> (A,B),(B,C),(A,C) =sym=> (A,B),(B,A),(B,C),(C,B),(A,C),(C,A)
A-->B-->C : (A,B),(B,C) =sym=> (A,B),(B,A),(B,C),(C,B) =tran=> (A,B),(B,A),(A,A),(B,C),(C,B),(B,B),(A,C),(C,A),(C,C)
closures directed-acyclic-graphs associativity symmetric transitive-closure
closures directed-acyclic-graphs associativity symmetric transitive-closure
asked Nov 12 '18 at 12:54
Radio ControlledRadio Controlled
19010
asked Nov 12 '18 at 12:54
Radio ControlledRadio Controlled
19010
asked Nov 12 '18 at 12:54
Radio ControlledRadio Controlled
19010
asked Nov 12 '18 at 12:54
Radio ControlledRadio Controlled
19010
asked Nov 12 '18 at 12:54
Radio ControlledRadio Controlled
19010
19010
add a comment |
add a comment |
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