  The extraction of templates such as ``regard X as Y'' from a set of related
phrases requires the identification of their internal structures. This paper
presents an unsupervised approach for extracting templates on-the-fly from only
tagged text by using a novel relaxed variant of the Sequence Binary Decision
Diagram (SeqBDD). A SeqBDD can compress a set of sequences into a graphical
structure equivalent to a minimal DFA, but more compact and better suited to
the task of template extraction. The main contribution of this paper is a
relaxed form of the SeqBDD construction algorithm that enables it to form
general representations from a small amount of data. The process of compression
of shared structures in the text during Relaxed SeqBDD construction, naturally
induces the templates we wish to extract. Experiments show that the method is
capable of high-quality extraction on tasks based on verb+preposition templates
from corpora and phrasal templates from short messages from social media.
