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How to determine if a binary relation R on M is a bisimulation?

  1. Feb 14, 2008 #1
    Let M be a system (possibly proper class-sized directed graph where the class of children of a given node is a set). A binary relation R on M is a BISIMULATION if [tex]R\subset R'[/tex], where for [tex]a, b\in M[/tex]

    [tex]aR'b \Leftrightarrow ((\forall x \in a_M\exists y\in b_M xRy) \wedge (\forall x \in b_M\exists y\in a_M xRy))[/tex]

    where [tex]a_M[/tex] is the set of children of a in M.

    So let ~ be the relation on the class of all sets V such that a~b iff there exists an accessible pointed graph that is the picture of both a and b.

    An accessible pointed graph is a directed graph with a distinguished node from where every other node is connected by a path.

    Show that ~ is a bisimulation.

    I'm not sure what bisimulation says. Can someone explain it in more familiar terms?
  2. jcsd
  3. Mar 1, 2008 #2
    The wording above (quoted from the book) is very bad. It took me a long time to understand that R is a bisimulation if R is contained in the ' operation.
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