Exact XML type checking in polynomial time

Abstract. Stay macro tree transducers (smtts) are an expressive formalism for reasoning about XSLT-like document transformations. Here, we consider the ex-act type checking problem for smtts. While the problem is decidable, the involved technique of inverse type inference is known to have exponential worst-case com-plexity (already for top-down transformations without parameters). We present a new adaptive type checking algorithm based on forward type inference through exact characterizations of output languages. The new algorithm correctly type-checks all call-by-value smtts. Given that the output type is specified by a de-terministic automaton, the algorithm is polynomial-time whenever the transducer uses only few parameters and visits every input node only constantly often. Our new approach can also be generalized from smtts to stay macro forest transducers which additionally support concatenation as built-in output operation.