tag:blogger.com,1999:blog-5659270781112607019.post3321358260199070573..comments2015-07-30T00:16:39.251-07:00Comments on Mathematical Linguistics etc.: Natural languages are SPARSE?Sean Fulophttp://www.blogger.com/profile/06610398963994746965noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5659270781112607019.post-57091544922112368872015-07-30T00:16:39.251-07:002015-07-30T00:16:39.251-07:00OK, this conjectured property of natural languages...OK, this conjectured property of natural languages was clarified somewhat at the recent Mathematics of Languages workshop. The idea is that the finite slice L^n of natural language L has a cardinality which is a "slowly growing" function of n, so that the cardinality ratio over the slice \Sigma^n of *all* expressions decreases to zero as n goes to infinity. But again, this is only *conjectured* to be a property of natural languages, and there seem to be no results known in formal language theory which pertain to such a notion. We're going to work it soon, I hope.Sean Fulophttps://www.blogger.com/profile/06610398963994746965noreply@blogger.comtag:blogger.com,1999:blog-5659270781112607019.post-40929344104943156132015-06-26T03:07:29.744-07:002015-06-26T03:07:29.744-07:00That is probably too strong. Say we have k proper ...That is probably too strong. Say we have k proper names n1 to nk, then the set of sentences of the form<br />n likes n and n likes n and .... repeated m times, <br />is a set of sentences of length 4m -1 which contains k^2m examples.<br />Alex Clarkhttps://www.blogger.com/profile/04634767958690153584noreply@blogger.com