Tree Transducers Research Articles

Toward Security Verification against Inference Attacks on Data Trees

This paper describes our ongoing work on security verification against inference attacks on data trees. We focus on infinite secrecy against inference attacks, which means that attackers cannot narrow down the candidates for the value of the sensitive information to finite by available information to the attackers. Our purpose is to propose a model under which infinite secrecy is decidable. To be specific, we first propose tree transducers which are expressive enough to represent practical queries. Then, in order to represent attackers' knowledge, we propose data tree types such that type inference and inverse type inference on those tree transducers are possible with respect to data tree types, and infiniteness of data tree types is decidable.

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.

Expressiveness of Visibly Pushdown Transducers

Visibly pushdown transducers (VPTs) are visibly pushdown automata extended with outputs. They have been introduced to model transformations of nested words, i.e. words with a call/return structure. As trees and more generally hedges can be linearized into (well) nested words, VPTs are a natural formalism to express tree transformations evaluated in streaming. This paper aims at characterizing precisely the expressive power of VPTs with respect to other tree transducer models.

Decoding Optimization in Tree Transducer based Translation Model

Decoding Optimization in Tree Transducer based Translation Model

An input–output hidden Markov model for tree transductions

The paper introduces an input-driven generative model for tree-structured data that extends the bottom-up hidden tree Markov model to non-homogeneous state transition and emission probabilities. We show how the proposed input-driven approach can be used to realize different types of structured transductions between trees. A thorough experimental analysis is proposed to investigate the advantage of introducing an input-driven dynamics in structured-data processing. The results of this analysis suggest that input-driven models can capture more discriminative structural information than homogeneous approaches in computational learning tasks, including document classification and more general substructure categorization.

Attribute grammars as tree transducers over cyclic representations of infinite trees and their descriptional composition

Evaluation of attributes w.r.t. an attribute grammar can be obtained by inductively computing a function expressing the dependencies of the synthesized attributes on inherited attributes. This higher-order functional approach to attribute evaluation can straightforwardly be implemented in a higher-order lazy functional language like Haskell. The resulting evaluation functions are, however, not easily amenable to optimization when we want to compose two attribute grammars. We present an alternative first-order functional interpretation of attribute grammars where the input tree is replaced by an extended cyclic tree each node of which is aware of its context viewed as an additional child tree. These cyclic representations of zippers (trees with their context) are natural generalizations of doubly-linked lists to trees over an arbitrary signature. Then we show that, up to that representation, descriptional composition of attribute grammars reduces to the composition of tree transducers.

Attribute grammars as tree transducers over cyclic representations of infinite trees and their descriptional composition

Attribute grammars as tree transducers over cyclic representations of infinite trees and their descriptional composition

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.

On the String Translations Produced by Multi Bottom–Up Tree Transducers

Tree transducers are defined as relations between trees, but in syntax-based machine translation, we are ultimately concerned with the relations between the strings at the yields of the input and output trees. We examine the formal power of Multi Bottom-Up Tree Transducers from this point of view.

Statistical Translation After Source Reordering: Oracles, Context-Aware Models, and Empirical Analysis

AbstractIn source reordering the order of the source words is permuted to minimize word order differences with the target sentence and then fed to a translation model. Earlier work highlights the benefits of resolving long-distance reorderings as a pre-processing step to standard phrase-based models. However, the potential performance improvement of source reordering and its impact on the components of the subsequent translation model remain unexplored. In this paper we study both aspects of source reordering. We set up idealized source reordering (oracle) models with/without syntax and present our own syntax-driven model of source reordering. The latter is a statistical model of inversion transduction grammar (ITG)-like tree transductions manipulating a syntactic parse and working with novel conditional reordering parameters. Having set up the models, we report translation experiments showing significant improvement on three language pairs, and contribute an extensive analysis of the impact of source reordering (both oracle and model) on the translation model regarding the quality of its input, phrase-table, and output. Our experiments show that oracle source reordering has untapped potential in improving translation system output. Besides solving difficult reorderings, we find that source reordering creates more monotone parallel training data at the back-end, leading to significantly larger phrase tables with higher coverage of phrase types in unseen data. Unfortunately, this nice property does not carry over to tree-constrained source reordering. Our analysis shows that, from the string-level perspective, tree-constrained reordering might selectively permute word order, leading to larger phrase tables but without increase in phrase coverage in unseen data.

Polynomial-time inverse computation for accumulative functions with multiple data traversals

The problem of inverse computation has many potential applications such as serialization/deserialization, providing support for undo, and test-case generation for software testing. In this paper, we propose an inverse computation method that always terminates for a class of functions known as parameter-linear macro tree transducers, which involve multiple data traversals and the use of accumulations. The key to our method is the observation that a function in the class can be regarded as a non-accumulative context-generating transformation without multiple data traversals. Accordingly, we demonstrate that it is easy to achieve terminating inverse computation for the class by context-wise memoization of the inverse computation results. We also show that when we use a tree automaton to express the inverse computation results, the inverse computation runs in time polynomial to the size of the original output and the textual program size.

EARLIEST NORMAL FORM AND MINIMIZATION FOR BOTTOM-UP TREE TRANSDUCERS

We show that for every deterministic bottom-up tree transducer, a unique equivalent transducer can be constructed which is minimal. The construction is based on a sequence of normalizing transformations which, among others, guarantee that non-trivial output is produced as early as possible. For a deterministic bottom-up transducer where every state produces either none or infinitely many outputs, the minimal transducer can be constructed in polynomial time.

Widening techniques for regular tree model checking

We consider the framework of regular tree model checking where sets of configurations of a system are represented by regular tree languages and its dynamics is modeled by a term rewriting system (or a regular tree transducer). We focus on the computation of the reachability set R*(L) where R is a regular tree transducer and L is a regular tree language. The construction of this set is not possible in general. Therefore, we present a general acceleration technique, called regular tree widening which allows to speed up the convergence of iterative fixpoint computations in regular tree model checking. This technique can be applied uniformly to various kinds of transformations. We show the application of our framework to different analysis contexts: verification of parameterized tree networks and data-flow analysis of multithreaded programs. Parametrized networks are modeled by relabeling tree transducers, and multithreaded programs are modeled by term rewriting rules encoding transformations on control structures. We prove that our widening technique can emulate many existing algorithms for special classes of transformations and we show that it can deal with transformations beyond the scope of these algorithms.

An alternative to synchronous tree substitution grammars

AbstractSynchronous tree substitution grammars (stsg) are a (formal) tree transformation model that is used in the area of syntax-based machine translation. A competitor that is at least as expressive as stsg is proposed and compared to stsg. The competitor is the extended multi bottom-up tree transducer (mbot), which is the bottom-up analogue with the additional feature that states have non-unary ranks. Unweighted mbot have already been investigated with respect to their basic properties, but the particular properties of the constructions that are required in the machine translation task are largely unknown. stsg and mbot are compared with respect to binarization, regular restriction, and application. Particular attention is paid to the complexity of the constructions.

Survey: Weighted Extended Top-down Tree Transducers Part II—Application in Machine Translation

In this second part of the survey, we present the application of weighted extended top-down tree transducers in machine translation, which is the automatic translation of natural language texts. We present several formal properties that are relevant to machine translation and evaluate the weighted extended top-down tree transducer along those criteria. In addition, we demonstrate how to extract rules for an extended top-down tree transducer from existing linguistic data and how to obtain suitable rule weights automatically from similar information. Overall, the aim of the survey is twofold. It should provide a synopsis that illustrates how theory (tree transducers) and practice (machine translation) interact on this particular example. Secondly, it presents a uniform and simplified treatment of the rule extraction and training algorithms that is accessible to the nonexpert. Additional details can be found in the original results that are referenced throughout the text.

Weighted Extended Tree Transducers

Weighted extended tree transducers (wxtts) over countably complete semirings are systematically explored. It is proved that the extension in the left-hand sides of a wxtt can be simulated by the inverse of a linear and nondeleting tree homomorphism. In addition, a characterization of the class of weighted tree transformations computable by bottom-up wxtts in terms of bimorphisms is provided. Backward and forward application to recognizable weighted tree languages are standard operations for wxtts. It is shown that the backward application of a linear wxtt preserves recognizability and that the domain of an arbitrary bottom-up wxtt is recognizable. Examples demonstrate that neither backward nor forward application of arbitrary wxtts preserves recognizability. Finally, a HASSE diagram relates most of the important subclasses of weighted tree transformations computable by wxtts.

Survey: Weighted Extended Top-down Tree Transducers Part I - Basics and Expressive Power

Weighted extended top-down tree transducers (transducteurs généralisés descendants [Arnold, Dauchet: Bi-transductions de forêts. ICALP'76. Edinburgh University Press, 1976]) received renewed interest in the field of Natural Language Processing, where they are used in syntax-based machine translation. This survey presents the foundations for a theoretical analysis of weighted extended top-down tree transducers. In particular, it discusses essentially complete semirings, which are a novel concept that can be used to lift incomparability results from the unweighted case to the weighted case even in the presence of infinite sums. In addition, several equivalent ways to define weighted extended top-down tree transducers are presented and the individual benefits of each presentation is shown on a small result.

PROPERTIES OF QUASI-RELABELING TREE BIMORPHISMS

The fundamental properties of the class QUASI of quasi-relabeling relations are investigated. A quasi-relabeling relation is a tree relation that is defined by a tree bimorphism (φ, L, ψ), where φ and ψ are quasi-relabeling tree homomorphisms and L is a regular tree language. Such relations admit a canonical representation, which immediately also yields that QUASI is closed under finite union. However, QUASI is not closed under intersection and complement. In addition, many standard relations on trees (e.g., branches, subtrees, v-product, v-quotient, and f-top-catenation) are not quasi-relabeling relations. If quasi-relabeling relations are considered as string relations (by taking the yields of the trees), then every Cartesian product of two context-free string languages is a quasi-relabeling relation. Finally, the connections between quasi-relabeling relations, alphabetic relations, and classes of tree relations defined by several types of top-down tree transducers are presented. These connections yield that quasi-relabeling relations preserve the regular and algebraic tree languages.

A pumping lemma for output languages of attributed tree transducers

A pumping lemma for output languages of attributed tree transducers

Implementation of a deterministic partial E-unification algorithm for macro tree transducers

Implementation of a deterministic partial E-unification algorithm for macro tree transducers