Node Query Preservation for Deterministic Linear Top-Down Tree Transducers

Abstract

SUMMARYThis paper discusses the decidability of node query preservation problems for tree transducers. We assume a transformation given by a deterministic linear top-down data tree transducer (abbreviated as DLT V ) and an n-ary query based on runs of a tree automaton. We say that a DLT V Tr strongly preserves a query Q if there is a query Q such that for every tree t, the answer set of Q for Tr(t) is equal to the answer set of Q for t. We also say that Tr weakly preserves Q if there is a query Q such that for every t, the answer set of Q for Tr(t) includes the answer set of Q for t. We show that the weak preservation problem is coNP-complete and the strong preservation problem is in 2-EXPTIME. We also show that the problems are decidable when a given transducer is a functional extended linear top-down data tree transducer with regular look-ahead, which is a more expressive transducer than DLT V .

Query Rewriting for Nondeterministic Tree Transducers

“…Similarly, in [5] both queries and views are n-ary node-selecting queries represented by tree automata. In [8], a hybrid approach was adopted, that is, for views tree transducers were used and for queries n-ary node-selecting queries were adopted. In [8], query preservation was shown to be decidable if a given transducer is a single-valued extended linear top-down tree transducer with regular look-ahead and a given query is a run-based n-ary node-selecting query.…”

“…In [8], a hybrid approach was adopted, that is, for views tree transducers were used and for queries n-ary node-selecting queries were adopted. In [8], query preservation was shown to be decidable if a given transducer is a single-valued extended linear top-down tree transducer with regular look-ahead and a given query is a run-based n-ary node-selecting query. The result in [19] is for deterministic tree transducers that require "origin" information.…”

“…The case when both views and queries are singlevalued (or deterministic) tree transducers was studied in [7], [10]. Single-valued tree transducers output just one tree for each input tree (see [7], [8], [10]). Our main contribution is to extend their results to nondeterministic tree transducers as views, which transform each input tree to a set of output trees.…”