Mathematically, Quirk, Brockett, and Dolan's approach to sentential paraphrase generation may be expressed in terms of the typical channel model equation for statistical machine translation: The equation denotes the search for the optimal paraphrase E p for a given sentence E. We may use Bayes' Theorem to rewrite this as: where P(E p ) is an n-gram language model providing a probabilistic estimate of the fluency of a hypothesis E p and P(E|E p ) is the translation model, or more appropriately for paraphrasing, the replacement model, providing a probabilistic estimate of what is essentially the semantic adequacy of the hypothesis paraphrase.
in addition, keyword-based heuristics need to be employed to prevent inaccurate merging of constituent nodes due to, say, alternations of active and passive voices among the The merging algorithm.