Efficient Factorization of Synchronous Context-Free Grammars

Factoring a Synchronous Context-Free Grammar into an equivalent grammar with a smaller number of nonterminals in each rule enables more efficient strategies for synchronous parsing. We present an algorithm for factoring an n-ary SCFG into a k-ary grammar in time O(kn). We also show how to efficiently compute the exact number of k-ary parsable permutations of length n, and discuss asymptotic behavior as n grows. The number of length n permutations that are k-ary parsable approaches a fixed ratio between successive terms as n grows for fixed k. As k grows, the difference between successive ratios approaches 1/e. The University of Rochester Computer Science Department supported this work.