--- Lars Henrik Mathiesen <[EMAIL PROTECTED]> wrote: > > Date: Mon, 01 Jul 2002 16:21:26 -0700 > > From: Rick Klement <[EMAIL PROTECTED]> > > > > Phil Carmody wrote: > > > --- Rick Klement <[EMAIL PROTECTED]> wrote: > > > > "Nodes that are isolated nodes (the name appears twice on the > > > > same line), can also be in a relationship to other nodes." > > > > > > But does that make them cycles or not? > > > > Having the same name appears twice on the same line does NOT make > a cycle. > > I think the real problem is the term isolated node. > > An true isolated node would be one that has no relation with other > nodes in the input partial order --- and it's true that the only > way > to input such a node is to give its relation to itself. > > However, by the definition of partial order (reflexive, > antisymmetric, > transitive), all nodes have such a relation --- which does not > create > a cycle --- but it can be omitted (inferred) if the node is > mentioned > in other relations. The question then is if it must be omitted in > that > case: and you answer no.
If the relation is a partial order, and reflexive, then the following needs changing: <<< There may be no possible order of nodes that will satisfy the input line requirements (the nodes contain a cycle). In this case, the program shall exit with a non-zero exit code. >>> because a b b a is satisfied by a b and b a in every model. i.e. It is explicitly _not_ the case that "no possible order of nodes [...] will satisfy the input line requirements". Phil ===== -- "One cannot delete the Web browser from KDE without losing the ability to manage files on the user's own hard disk." - Prof. Stuart E Madnick, MIT. So called "expert" witness for Microsoft. 2002/05/02 __________________________________________________ Do You Yahoo!? Sign up for SBC Yahoo! Dial - First Month Free http://sbc.yahoo.com
