Bottom-up automata on data trees and vertical XPath

A data tree is a finite tree whose every node carries a label from a finite alphabet and a datum from some infinite domain. We introduce a new model of automata over unranked data trees with a decidable emptiness problem. It is essentially a bottom-up alternating automaton with one register that can store one data value and can be used to perform equality tests with the data values occurring within the subtree of the current node. We show that it captures the expressive power of the vertical fragment of XPath - containing the child, descendant, parent and ancestor axes - obtaining thus a decision procedure for its satisfiability problem

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.Comment: In Proceedings TTATT 2013, arXiv:1311.505

FO2(<,+1,~) on data trees, data tree automata and branching vector addition systems

A data tree is an unranked ordered tree where each node carries a label from a finite alphabet and a datum from some infinite domain. We consider the two variable first order logic FO2(<,+1,~) over data trees. Here +1 refers to the child and the next sibling relations while < refers to the descendant and following sibling relations. Moreover, ~ is a binary predicate testing data equality. We exhibit an automata model, denoted DAD# that is more expressive than FO2(<,+1,~) but such that emptiness of DAD# and satisfiability of FO2(<,+1,~) are inter-reducible. This is proved via a model of counter tree automata, denoted EBVASS, that extends Branching Vector Addition Systems with States (BVASS) with extra features for merging counters. We show that, as decision problems, reachability for EBVASS, satisfiability of FO2(<,+1,~) and emptiness of DAD# are equivalent

Hindering data theft with encrypted data trees

Data theft is a major threat for modern organizations with potentially large economic consequences. Although these attacks may well originate outside an organization’s information systems, the attacker—or else an insider—must even-tually make contact with the system where the information resides and extract it. In this work, we propose a scheme that hinders unauthorized data extraction by modifying the basic file system primitives used to access files. Intuitively, our proposal emulates the chains used to protect valuable items in certain clothing shopping centers, where shoplifting is prevented by forcing the thief to steal the whole rack of items. We achieve this by encrypting sensitive files using nonces (i.e., pseudorandom numbers used only once) as keys. Such nonces are available, also in encrypted form, in other objects of the file system. The system globally resembles a distributed Merkle hash tree, in such a way that getting access to a file requires previous access to a number of other files. This forces any potential attacker to extract not only the targeted sensitive information, but also all the files chained to it that are necessary to compute the associated key. Further-more, our scheme incorporates a probabilistic rekeying mechanism to limit the damage that might be caused by patient extractors. We report experimental results measuring the time overhead introduced by our proposal and compare it with the effort an attacker would need to successfully extract information from the system. Our results show that the scheme increases substantially the effort required by an insider, while the introduced overhead is feasible for standard computing platforms

Containment of Pattern-Based Queries over Data Trees

International audienceWe study static analysis, in particular the containment problem, for analogs of conjunctive queries over XML documents. The problem has been studied for queries based on arbitrary patterns, not necessarily following the tree structure of documents. However, many applications force the syntactic shape of queries to be tree-like, as they are based on proper tree patterns. This renders previous results, crucially based on having non-tree-like features, inapplicable. Thus, we investigate static analysis of queries based on proper tree patterns. We go beyond simple navigational conjunctive queries in two ways: we look at unions and Boolean combinations of such queries as well and, crucially, all our queries handle data stored in documents, i.e., we deal with containment over data trees. We start by giving a general \Pi^p_2 upper bound on the containment of conjunctive queries and Boolean combinations for patterns that involve all types of navigation through documents. We then show matching hardness for conjunctive queries with all navigation, or their Boolean combinations with the simplest form of navigation. After that we look at cases when containment can be witnessed by homomorphisms of analogs of tableaux. These include conjunctive queries and their unions over child and next-sibling axes; however, we show that not all cases of containment can be witnessed by homomorphisms. We look at extending tree patterns used in queries in three possible ways: with wildcard, with schema information, and with data value comparisons. The first one is relatively harmless, the second one tends to increase complexity by an exponential, and the last one quickly leads to undecidability

Exploratory analysis of marketing data: trees vs. regression

This article compares the predictive ability of models developed by two different statistical methods, tree analysis and regression analysis. Each was used in an exploratory study to develop a model to make predictions for a specific marketing situation

A Sequent Calculus for a Modal Logic on Finite Data Trees

We investigate the proof theory of a modal fragment of XPath equipped with data (in)equality tests over finite data trees, i.e., over finite unranked trees where nodes are labelled with both a symbol from a finite alphabet and a single data value from an infinite domain. We present a sound and complete sequent calculus for this logic, which yields the optimal PSPACE complexity bound for its validity problem