We describe a syntax-based algorithm that automatically builds Finite State Automata (word lattices) from semantically equivalent translation sets. These FSAs are good representations of paraphrases. They can be used to extract lexical and syntactic paraphrase pairs and to generate new, unseen sentences that express the same meaning as the sentences in the input sets. Our FSAs can also predict the correctness of alternative semantic renderings, which may be used to evaluate the quality of translations.