The original ACL-06 paper gives an overview of the GHKM paper, which I ended up cramping into just two paragraphs due to constraints on space. I made slight changes to the terminology of GHKM (which I mentioned in a footnote) to avoid the need to define the closure of a span (i.e., span(closure(n))). Unfortunately, this new presentation of GHKM leads to a different behavior in some cases. Thanks to Liang Huang and Smaranda Muresan for pointing out an inconsistency in the paper. My home page links to a revised version of the paper that addresses this issue, and that uses a terminology that is fully consistent with the NAACL-04 paper. No other changes were made: http://cs.stanford.edu/~mgalley/papers/acl06-sbtm.pdf The original ACL-06 paper is here: http://cs.stanford.edu/~mgalley/papers/acl06-sbtm-original.pdf For readers interested in a detailed comparison, an explanation follows. -------------------------------------------------------------------------- * Definitions in the NAACL-04 paper: span(n): the set of words in f (the source sentence) that are reachable from n. closure(span(n)): the shortest contiguous span that is a superset of span(n) complement-span(n): the union of the spans of all nodes n' in the graph G that are neither descendants nor ancestors of n. (Note that GHKM does not explicitly use any definition of complement-span, but the notion is implicit). Frontier set F: the set of all nodes of G that satisfy: closure(span(n)) ^ complement-span(n) = \empty-set * Definitions in the ACL-06 paper: span(n): shorted contiguous span that includes both the first and last word in f reachable from n. complement-span(n): is the union of the spans of all nodes n' in the graph G that are neither descendants nor ancestors of n. Frontier set F: the set of all nodes of G that satisfy: span(n) ^ complement-span(n) = \empty-set * Comparison of ACL-06 with NAACL-04: ACL-06's definition of span(n) is equivalent to NAACL-04's definition of closure(span(n)), so the two conditions are seemingly equivalent: NAACL-04: closure(span(n)) ^ complement-span(n) = \empty-set ACL-06: span(n) ^ complement-span(n) = \empty-set The small catch is that the definition of complement-span(n) relies on the definition of span(n), which are different in the two papers. Hence, F in ACL-06 is sometimes different from F in NAACL-04. As mentioned previously, this problem has been fixed in the revision.