Top-down Tree Transducers Research Articles

Functionality of compositions of top-down tree transducers is decidable

We prove that functionality of compositions of top-down tree transducers is decidable by reducing the problem to the functionality of one top-down tree transducer with look-ahead.

Compositions of Weighted Extended Tree Transducers — The Unambiguous Case

Generalizations of another two open conjectures, Conjectures 13 and 14, of [Lagoutte, Maletti: Survey — Weighted extended top-down tree transducers — Part III: Composition. Proc. AFCS, LNCS 7020, p. 272–308, Springer 2011] are verified. It is proved that the composition of an unambiguous weighted extended tree transducer [Formula: see text] with a nondeleting weighted top-down tree transducer [Formula: see text] can be computed by a single weighted extended tree transducer. Extending the recent confirmation of Conjecture 11 it is also proved that the composition succeeds for any weighted top-down tree transducer [Formula: see text] (even if it is not nondeleting) if the unambiguous weighted extended tree transducer [Formula: see text] is constant.

Compositions of Weighted Extended Top-Down Tree Transducers

Compositions of Weighted Extended Top-Down Tree Transducers

Definability Results for Top-Down Tree Transducers

Top-down tree transducers are well established formalism for describing tree translations. Such transducers can be further enhanced with look-ahead allowing them to inspect input subtrees before processing them. Oftentimes it is advantageous to know when the look-ahead can be eliminated and the translation be implemented by a simpler transducer. We show that for a given top-down transducer with look-ahead it is decidable whether or not its translation is definable (1) by a linear deterministic top-down tree transducer or (2) by a tree homomorphism. We present algorithms that construct equivalent such transducers if they exist. Our results also apply to bottom-up transducers as well as compositions of transducers.

Compositions with Constant Weighted Extended Tree Transducers

Conjecture 11 of [Lagoutte, Maletti: Survey — Weighted extended top-down tree transducers — Part III: Composition. Proc. AFCS, LNCS 7020, p. 272–308, Springer 2011] is confirmed. It is demonstrated that the composition of a constant weighted extended tree transducer with a linear weighted top-down tree transducer can be computed by a single weighted extended tree transducer. Whereas linearity and the top-down property are syntactic, the constant property is semantic. The decidability of the constant property is investigated in several restricted settings.

Streaming ranked-tree-to-string transducers

Streaming tree transducers with single-use restriction (STTsurs) were introduced by Alur and D'Antoni as an analyzable, executable, and expressive model for transforming unranked ordered trees in a single pass. The equivalence problem of STTsurs is decidable because their class is as expressive as the class of MSO-definable tree transformations. In this paper, we present streaming ranked-tree-to-string transducers (SRTSTs), based on STTsurs: SRTSTs are released from the single-use restriction while their input and output are restricted to ranked trees and strings, respectively. We show that the expressiveness of SRTSTs coincides with that of deterministic top-down tree transducers with regular look-ahead (yDTRs), whose equivalence problem is known to be decidable. Our proof is done by constructing equivalent transducers in both directions.

Decision problems of tree transducers with origin

A tree transducer with origin translates an input tree into a pair of output tree and origin information. The origin information maps each node in the output tree to the unique node in the input tree that created it. In this way, the implementation of the transducer becomes part of its semantics. We show that the landscape of decidable properties changes drastically when origin information is added. For instance, equivalence of nondeterministic top-down and MSO transducers with origin becomes decidable. Both problems are undecidable without origin. The equivalence of deterministic top-down tree-to-string transducers is decidable with origin, while without origin it has (until very recently) been a long standing open problem. With origin, we can decide if a deterministic macro tree transducer can be realized by a deterministic top-down tree transducer; without origin this is an open problem.

Synthesis of deterministic top-down tree transducers from automatic tree relations

We consider the synthesis of deterministic tree transducers from automaton definable specifications, given as binary relations, over finite trees. We consider the case of tree-automatic specifications, meaning the specification is recognizable by a top-down tree automaton that reads the two given trees synchronously in parallel. In this setting we study tree transducers that are allowed to have either delay that remains in a given bound or arbitrary delay. Delay is caused whenever the transducer reads a symbol from the input tree without producing output. For specifications that are deterministic top-down tree-automatic, we provide decision procedures for both bounded and arbitrary delay that yield deterministic top-down tree transducers which realize the specification for input trees that are part of the specification domain, and can behave arbitrarily on trees outside the domain. Similarly to the case of relations over words, we use two-player games as the main technique to obtain our results.

Composition Closure of Linear Extended Top-down Tree Transducers

Linear extended top-down tree transducers (or synchronous tree-substitution grammars) are popular formal models of tree transformations that are extensively used in syntax-based statistical machine translation. The expressive power of compositions of such transducers with and without regular look-ahead is investigated. In particular, the restrictions of ź-freeness, strictness, and nondeletion are considered. The composition hierarchy turns out to be finite for all ź-free (all rules consume input) variants of these transducers except for the nondeleting ź-free transducers. The least number of transducers needed for the full expressive power of arbitrary compositions is presented. In all remaining cases (incl. the nondeleting ź-free transducers) the composition hierarchy does not collapse.

Look-ahead removal for total deterministic top-down tree transducers

Top-down tree transducers are a convenient formalism for describing tree transformations. They can be equipped with regular look-ahead, which allows them to inspect a subtree before processing it. In certain cases, such a look-ahead can be avoided and the transformation can be realized by a transducer without look-ahead. Removing the look-ahead from a transducer, if possible, is technically highly challenging. For a restricted class of transducers with look-ahead, namely those that are total, deterministic, ultralinear, and bounded erasing, we present an algorithm that, for a given transducer from that class, (1) decides whether it is equivalent to a total deterministic transducer without look-ahead, and (2) constructs such a transducer if the answer is positive. For the whole class of total deterministic transducers with look-ahead we present a similar algorithm, which assumes that a so-called difference bound is known for the given transducer. The designer of a transducer can usually also determine a difference bound for it.

A Survey on Decidable Equivalence Problems for Tree Transducers

The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree transducers, (2) linear size increase, i.e., MSO definable tree transducers, and (3) monadic input and output ranked alphabets. For the full class of mtts, decidability of equivalence remains a long-standing open problem.

The Power of Weighted Regularity-Preserving Multi Bottom-Up Tree Transducers

The expressive power of regularity-preserving [Formula: see text]-free weighted linear multi bottom-up tree transducers is investigated. These models have very attractive theoretical and algorithmic properties, but (especially in the weighted setting) their expressive power is not well understood. Despite the regularity-preserving restriction, their power still exceeds that of composition chains of [Formula: see text]-free weighted linear extended top-down tree transducers with regular look-ahead. The latter devices are a natural super-class of weighted synchronous tree substitution grammars, which are commonly used in syntax-based statistical machine translation. In particular, the linguistically motivated discontinuous transformation of topicalization can be modeled by such multi bottom-up tree transducers, whereas the mentioned composition chains cannot implement it. On the negative side, the inverse of topicalization cannot be implemented by any such multi bottom-up tree transducer, which confirms their bottom-up nature (and non-closure under inverses). An interesting, promising, and widely applicable proof technique is used to prove these statements.

Erratum to: “Top-down Tree Transducers with Regular Look-ahead”

In Theorem 3.2 of my paper [1] it is shown thatDB-FST ⊂ DTR-FST, whereDB-FST is the class of deterministic bottom-up finite state tree transformations and DTR-FST is the class of deterministic top-down finite state tree transformations with regular look-ahead (and ⊂ denotes proper inclusion). One may then ask for a characterization of DB-FST in terms of dtr-fst. In Theorem 3.2 of [1] it is wrongly stated that DB-FST = ODTR-FST, whereODTR-FST is the class of one-state dtr-fst. The correct statement is that DB-FST = FTA ◦ ODTR-FST,

Node Query Preservation for Deterministic Linear Top-Down Tree Transducers

This paper discusses the decidability of node query preservation problems for XML document transformations. 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 document t, the answer set of Q' for Tr(t) is equal to the answer set of Q for t. Also we say that Tr weakly preserves Q if there is a query Q' such that for every t_d in the range of Tr, the answer set of Q' for t_d is equal to the union of the answer set of Q for t such that t_d = Tr(t). We show that the weak preservation problem is coNP-complete and the strong preservation problem is in 2-EXPTIME.

An XSLT Transformation Method for Distributed XML

Recently, the sizes of XML documents have rapidly been increasing. Distributed XML is a novel form of XML document, in which an XML document is partitioned into fragments and managed separately in plural sites. Distributed XML documents can often be managed more easily than a single large document, due to geographical and/or administrative factors. In this paper, we propose a method for performing XSLT transformation efficiently for distributed XML documents. We assume that the expressive power of XSLT is restricted to an extended version of unranked top-down tree transducer. Our basic strategy is to transform all the XML fragments in parallel. We implemented our method in Ruby and made evaluation experiments. This result suggests that our method is more efficient than a centralized approach.

Synthesis of Deterministic Top-down Tree Transducers from Automatic Tree Relations

We consider the synthesis of deterministic tree transducers from automaton definable specifications, given as binary relations, over finite trees. We consider the case of specifications that are deterministic top-down tree automatic, meaning the specification is recognizable by a deterministic top-down tree automaton that reads the two given trees synchronously in parallel. In this setting we study tree transducers that are allowed to have either bounded delay or arbitrary delay. Delay is caused whenever the transducer reads a symbol from the input tree but does not produce output. We provide decision procedures for both bounded and arbitrary delay that yield deterministic top-down tree transducers which realize the specification for valid input trees. Similar to the case of relations over words, we use two-player games to obtain our results.

Equivalence Problems for Tree Transducers: A Brief Survey

The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree transducers, (2) linear size increase, i.e., MSO definable tree transducers, and (3) monadic input and output ranked alphabets. For the full class of MTTs, decidability of equivalence remains a long-standing open problem.

Checking Time Linearity of Regular Expression Matching Based on Backtracking

Most implementations of regular expression matching in programming languages are based on backtrack- ing. With this implementation strategy, matching may not be achieved in linear time with respect to the length of the input. In the worst case, it may take exponential time. In this paper, we propose a method of checking whether or not regular expression matching runs in linear time. We construct a top-down tree transducer with regular lookahead that translates the input string into a tree corresponding to the execution steps of matching based on backtracking. The regular expression matching then runs in linear time if the tree transducer is of linear size increase. To check this property of the tree transducer, we apply a result of Engelfriet and Maneth. We implemented the method in OCaml and conducted experiments that checked the time linearity of regular expressions appearing in several popular PHP programs. Our implementation showed that 47 of 393 regular expressions were not linear.

Node Query Preservation for Deterministic Linear Top-Down Tree Transducers

This paper discusses the decidability of node query preservation problems for XML document transformations. 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 document t, the answer set of Q' for Tr(t) is equal to the answer set of Q for t. Also we say that Tr weakly preserves Q if there is a query Q' such that for every t_d in the range of Tr, the answer set of Q' for t_d is equal to the union of the answer set of Q for t such that t_d = Tr(t). We show that the weak preservation problem is coNP-complete and the strong preservation problem is in 2-EXPTIME.

Deciding Schema <i>k</i>-Secrecy for XML Databases

We study a static analysis problem on k-secrecy, which is a metric for the security against inference attacks on XML databases. Intuitively, k-secrecy means that the number of candidates of sensitive data of a given database instance or the result of unauthorized query cannot be narrowed down to k-1 by using available information such as authorized queries and their results. In this paper, we investigate the decidability of the schema k-secrecy problem defined as follows: for a given XML database schema, an authorized query and an unauthorized query, decide whether every database instance conforming to the given schema is k-secret. We first show that the schema k-secrecy problem is undecidable for any finite k>1 even when queries are represented by a simple subclass of linear deterministic top-down tree transducers (LDTT). We next show that the schema ∞-secrecy problem is decidable for queries represented by LDTT. We give an algorithm for deciding the schema ∞-secrecy problem and analyze its time complexity. We show the schema ∞-secrecy problem is EXPTIME-complete for LDTT. Moreover, we show similar results LDTT with regular look-ahead.