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 efcient 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 efciently compute the exact number of k-ary parsable permutations of length n, and discuss asymptotic behavior as n grows.