Linear Bounded Composition of Tree-Walking Tree Transducers: Linear Size Increase and Complexity

Compositions of tree-walking tree transducers form a hierarchy with respect to the number of transducers in the composition. As main technical result it is proved that any such composition can be realized as a linear bounded composition, which means that the sizes of the intermediate results can be chosen to be at most linear in the size of the output tree. This has consequences for the expressiveness and complexity of the translations in the hierarchy. First, if the computed translation is a function of linear size increase, i.e., the size of the output tree is at most linear in the size of the input tree, then it can be realized by just one, deterministic, tree-walking tree transducer. For compositions of deterministic transducers it is decidable whether or not the translation is of linear size increase. Second, every composition of deterministic transducers can be computed in deterministic linear time on a RAM and in deterministic linear space on a Turing machine, measured in the sum of the sizes of the input and output tree. Similarly, every composition of nondeterministic transducers can be computed in simultaneous polynomial time and linear space on a nondeterministic Turing machine. Their output tree languages are deterministic context-sensitive, i.e., can be recognized in deterministic linear space on a Turing machine. The membership problem for compositions of nondeterministic translations is nondeterministic polynomial time and deterministic linear space. The membership problem for the composition of a nondeterministic and a deterministic tree-walking tree translation (for a nondeterministic IO macro tree translation) is log-space reducible to a context-free language, whereas the membership problem for the composition of a deterministic and a nondeterministic tree-walking tree translation (for a nondeterministic OI macro tree translation) is possibly NP-complete

The Equivalence Problem for Deterministic MSO Tree Transducers is Decidable

It is decidable for deterministic MSO definable graph-to-string or graph-to-tree transducers whether they are equivalent on a context-free set of graphs

XQuery Streaming by Forest Transducers

Streaming of XML transformations is a challenging task and only very few systems support streaming. Research approaches generally define custom fragments of XQuery and XPath that are amenable to streaming, and then design custom algorithms for each fragment. These languages have several shortcomings. Here we take a more principles approach to the problem of streaming XQuery-based transformations. We start with an elegant transducer model for which many static analysis problems are well-understood: the Macro Forest Transducer (MFT). We show that a large fragment of XQuery can be translated into MFTs --- indeed, a fragment of XQuery, that can express important features that are missing from other XQuery stream engines, such as GCX: our fragment of XQuery supports XPath predicates and let-statements. We then rely on a streaming execution engine for MFTs, one which uses a well-founded set of optimizations from functional programming, such as strictness analysis and deforestation. Our prototype achieves time and memory efficiency comparable to the fastest known engine for XQuery streaming, GCX. This is surprising because our engine relies on the OCaml built in garbage collector and does not use any specialized buffer management, while GCX's efficiency is due to clever and explicit buffer management.Comment: Full version of the paper in the Proceedings of the 30th IEEE International Conference on Data Engineering (ICDE 2014

Deciding Linear Height and Linear Size-to-Height Increase for Macro Tree Transducers

In this paper we study Macro Tree Transducers (MTT), specifically the Linear Height Increase ("LHI") and Linear input Size to output Height ("LSHI") constraints. In order to decide whether a Macro tree transducer (MTT) is of LHI or LSHI, we define a notion of depth-properness: a MTT is depth-proper if, for each state, there is no bound to the depth at which it places its argument trees. We show how to effectively put a MTT in depth-proper form. For MTTs in Depth-proper form, we characterize the LSH property as equivalent to the finite-nesting property, and we characterize the LHI property as equivalent to the finiteness of a new type of nesting which we call Multi-Leaf-nesting (or ML-nesting). As opposed to regular nesting where we look at the nesting of states applied to a single input node, we count the nesting of states applied to nodes that are not ancestors of each other. We use this characterization to give a decision procedure for the LSHI and LHI properties. Finally we consider the decision problem of the LSOI (Linear input Size to number of distinct Output subtrees Increase) property. A long standing open problem is whether MTT of LSOI are as expressive as Attribute Tree Transducers (ATT), in this paper we show that deciding whether a MTT is of LSOI is as hard as deciding the equivalence of ATTs

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.Comment: In Proceedings AFL 2014, arXiv:1405.527

Modeling and Analyzing Systemic Risk in Complex Sociotechnical Systems The Role of Teleology, Feedback, and Emergence

Recent systemic failures such as the BP Deepwater Horizon Oil Spill, Global Financial Crisis, and Northeast Blackout have reminded us, once again, of the fragility of complex sociotechnical systems. Although the failures occurred in very different domains and were triggered by different events, there are, however, certain common underlying mechanisms of abnormalities driving these systemic failures. Understanding these mechanisms is essential to avoid such disasters in the future. Moreover, these disasters happened in sociotechnical systems, where both social and technical elements can interact with each other and with the environment. The nonlinear interactions among these components can lead to an “emergent” behavior – i.e., the behavior of the whole is more than the sum of its parts – that can be difficult to anticipate and control. Abnormalities can propagate through the systems to cause systemic failures. To ensure the safe operation and production of such complex systems, we need to understand and model the associated systemic risk. Traditional emphasis of chemical engineering risk modeling is on the technical components of a chemical plant, such as equipment and processes. However, a chemical plant is more than a set of equipment and processes, with the human elements playing a critical role in decision-making. Industrial statistics show that about 70% of the accidents are caused by human errors. So, new modeling techniques that go beyond the classical equipment/process-oriented approaches to include the human elements (i.e., the “socio” part of the sociotechnical systems) are needed for analyzing systemic risk of complex sociotechnical systems. This thesis presents such an approach. This thesis presents a new knowledge modeling paradigm for systemic risk analysis that goes beyond chemical plants by unifying different perspectives. First, we develop a unifying teleological, control theoretic framework to model decision-making knowledge in a complex system. The framework allows us to identify systematically the common failure mechanisms behind systemic failures in different domains. We show how cause-and-effect knowledge can be incorporated into this framework by using signed directed graphs. We also develop an ontology-driven knowledge modeling component and show how this can support decision-making by using a case study in public health emergency. This is the first such attempt to develop an ontology for public health documents. Lastly, from a control-theoretic perspective, we address the question, “how do simple individual components of a system interact to produce a system behavior that cannot be explained by the behavior of just the individual components alone?” Through this effort, we attempt to bridge the knowledge gap between control theory and complexity science

The very model of a modern linguist — in honor of Helge Dyvik

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