Efficient Evaluation Of Nondeterministic Automata Using Factorization Forests

In the first part of the paper, we propose an algorithm which inputs an NFA A and a word a(1) ... a(n), does a precomputation, and then answers queries of the form: "is the infix a(i) ... a(j) accepted by A?". The precomputation is in time poly(A) . n, and the queries are answered in time poly(A). This improves on previous algorithms that worked with the exponentially less succinct DFA's or monoids.In the second part of the paper, we propose a transducer model for data. trees. We show that the transducer can be evaluated in linear time. We use this result to evaluate XPath queries in linear time.The algorithms in both parts of the paper use factorization forests.