Querying parse trees of stochastic context-free grammars

Stochastic context-free grammars (SCFGs) have long been recognized as useful for a large variety of tasks including natural language processing, morphological parsing, speech recognition, information extraction, Web-page wrapping and even analysis of RNA. A string and an SCFG jointly represent a probabilistic interpretation of the meaning of the string, in the form of a (possibly infinite) probability space of parse trees. The problem of evaluating a query over this probability space is considered under the conventional semantics of querying a probabilistic database. For general SCFGs, extremely simple queries may have results that include irrational probabilities. But, for a large subclass of SCFGs (that includes all the standard studied subclasses of SCFGs) and the language of tree-pattern queries with projection (and child/descendant edges), it is shown that query results have rational probabilities with a polynomial-size bit representation and, more importantly, an efficient query-evaluation algorithm is presented.