Intercalation theorems for tree transducer languages

Abstract

We develop intercalation lemmas for the computations of the top-down tree transducers defined by Rounds [15] and Thatcher [17]. These lemmas are used to prove necessary conditions for languages all of whose strings are of exponential length to be tree transducer languages. The language {ww:w&egr;{a,b}*, ¦w¦=2n,n≥0}, which is generable by the composition of two transducers, is shown not to be generable by one. The proof technique applies to bottom-up transducers as well. The results are related to some subclasses of Woods' Augmented Transition Networks [18] characterized elsewhere in terms of tree transducer languages [14].