We consider the problem of evaluating in streaming (i.e., in a single left-to-right pass) a nested word transduction with a limited amount of memory. A transduction T is said to be height bounded memory (HBM) if it can be evaluated with a memory that depends only on the size of T and on the height of the input word. We show that it is decidable in coNPTime for a nested word transduction defined by a visibly pushdown transducer (VPT), if it is HBM. In this case, the required amount of memory may depend exponentially on the height of the word. We exhibit a sufficient, decidable condition for a VPT to be evaluated with a memory that depends quadratically on the height of the word. This condition defines a class of transductions that strictly contains all determinizable VPTs.
Cite
@article{arxiv.1707.00527,
title = {Streamability of nested word transductions},
author = {Emmanuel Filiot and Olivier Gauwin and Pierre-Alain Reynier and Frédéric Servais},
journal= {arXiv preprint arXiv:1707.00527},
year = {2023}
}