Order-Sorted Unification with Regular Expression Sorts

We extend first-order order-sorted unification by permitting regular expression sorts for variables and in the domains of function symbols. The set of basic sorts is finite. The obtained signature corresponds to a finite bottom-up hedge automaton. The unification problem in such a theory generalizes some known unification problems. Its unification type is infinitary. We give a complete unification procedure and prove decidability

Applications of rule-based programming to verification and transformation of XML

課題番号：2050002

Determinization and Minimization of Automata for Nested Words Revisited

International audienceWe consider the problem of determinizing and minimizing automata for nested words in practice. For this we compile the nested regular expressions ($NRE_s$) from the usual XPath benchmark to nested word automata ($NW$$A_s$). The determinization of these $NW$ $A_s$, however, fails to produce reasonably small automata. In the best case, huge deterministic $NW$$A_s$ are produced after few hours, even for relatively small $NRE_s$ of the benchmark. We propose a different approach to the determinization of automata for nested words. For this, we introduce stepwise hedge automata ($SHA_s$) that generalize naturally on both (stepwise) tree automata and on finite word automata. We then show how to determinize $SHA_s$, yielding reasonably small deterministic automata for the $NRE_s$ from the XPath benchmark. The size of deterministic $SHA_s$ automata can be reduced further by a novel minimization algorithm for a subclass of $SHA_s$. In order to understand why the new approach to determinization and minimization works so nicely, we investigate the relationship between $NWA_s$ and $SHA_s$ further. Clearly, deterministic $SHA_s$ can be compiled to deterministic NWAs in linear time, and conversely, $NW$$A_s$ can be compiled to nondeterministic $SHA_s$ in polynomial time. Therefore, we can use $SHA_s$ as intermediates for determinizing $NWA_s$, while avoiding the huge size increase with the usual determinization algorithm for $NWA_s$. Notably, the NWAs obtained from the $SHA_s$ perform bottom-up and left-to-right computations only, but no top-down computations. This $NWA$-behavior can be distinguished syntactically by the (weak) single-entry property, suggesting a close relationship between $SHA_s$ and single-entry $NWA_s$. In particular, it turns out that the usual determinization algorithm for $NWA_s$ behaves well for single-entry $NWA_s$, while it quickly explodes without the single-entry property. Furthermore, it is known that the class of deterministic multi-module single-entry $NWA_s$ enjoys unique minimization. The subclass of deterministic $SHA_s$ to which our novel minimization algorithm applies is different though, in that we do not impose multiple modules. As further optimizations for reducing the sizes of the constructed $SHA_s$, we propose schema-based cleaning and symbolic representations based on apply-else rules, that can be maintained by determinization. We implemented the optimizations and report the experimental results for the automata constructed for the XPathMark benchmark

Algebraic decoder specification: coupling formal-language theory and statistical machine translation: Algebraic decoder specification: coupling formal-language theory and statistical machine translation

The specification of a decoder, i.e., a program that translates sentences from one natural language into another, is an intricate process, driven by the application and lacking a canonical methodology. The practical nature of decoder development inhibits the transfer of knowledge between theory and application, which is unfortunate because many contemporary decoders are in fact related to formal-language theory. This thesis proposes an algebraic framework where a decoder is specified by an expression built from a fixed set of operations. As yet, this framework accommodates contemporary syntax-based decoders, it spans two levels of abstraction, and, primarily, it encourages mutual stimulation between the theory of weighted tree automata and the application

A proposal for 3d quantum gravity and its bulk factorization

Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT. This theory can be viewed as a $q$-deformation and dimensional uplift of JT gravity. Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes. In the conventional Chern-Simons description, these black holes correspond to Wilson lines in representations of \PSL(2,\mathbb{R})\otimes \PSL(2,\mathbb{R}) . We show that the correct calculation of gravitational entropy suggests we should interpret the bulk theory as an extended topological quantum field theory associated to the quantum semi-group \SL^+_{q}(2,\mathbb{R})\otimes \SL^+_{q}(2,\mathbb{R}). Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime.Comment: Appendix expanded. Discussion of extended TQFT is expanded and moved to section 6. Added discussion of entropy formula in eq 4.2, comparison to Liouville theory below eq 2.41, and expanded remarks on relation to Teichmuller TQFT in section 6.4 and section

Optimization with Sparsity-Inducing Penalties

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate non-smooth norms. The goal of this paper is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted $\ell_2$-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view

BEYOND CLASSICAL CAUSAL MODELS: PATH DEPENDENCE, ENTANGLED MISSINGNESS AND GENERALIZED COARSENING

Classical causal models generally assume relatively simple settings like static observations, complete observability and independent and identically distributed (i.i.d.) data samples. For many systems of scientific interest, such assumptions are unrealistic. More recent work has explored models with complex properties including (time-invariant) temporal dynamics, data dependence, as well as missingness within the causal inference framework. Inspired by these advances, this dissertation goes beyond these classical causal inference models to explore the following complications that can arise in some causal systems – (i) path dependence, whereby systems exhibit state-specific causal relationships and a temporal evolution that could be counterfactually altered, (ii) entangled missingness, where missingness occurs in data together with causal dependence and finally, (iii) generalized coarsening, where systems entail causal processes operating at multiple timescales, and estimands of interest lie at a timescale different from that in which data is observed. In particular, we use the language of graphical causal models and discuss an important component of the causal inference pipeline, namely identification, which links the counterfactual of interest to the observed data via a set of assumptions. In some cases, we also discuss estimation, which allows us to obtain identified parameters from finite samples of data. We illustrate the use of these novel models on observational data obtained from biomedical and clinical settings

Belief Propagation approach to epidemics prediction on networks

In my thesis I study the problem of predicting the evolution of the epidemic spreading on networks when incomplete information, in form of a partial observation, is available. I focus on the irreversible process described by the discrete time version of the Susceptible-Infected-Recovered (SIR) model on networks. Because of its intrinsic stochasticity, forecasting the SIR process is very difficult, even if the structure of individuals contact pattern is known. In today's interconnected and interdependent society, infectious diseases pose the threat of a worldwide epidemic spreading, hence governments and public health systems maintain surveillance programs to report and control the emergence of new disease event ranging from the seasonal influenza to the more severe HIV or Ebola. When new infection cases are discovered in the population it is necessary to provide real-time forecasting of the epidemic evolution. However the incompleteness of accessible data and the intrinsic stochasticity of the contagion pose a major challenge. The idea behind the work of my thesis is that the correct inference of the contagion process before the detection of the disease permits to use all the available information and, consequently, to obtain reliable predictions. I use the Belief Propagation approach for the prediction of SIR epidemics when a partial observation is available. In this case the reconstruction of the past dynamics can be efficiently performed by this method and exploited to analyze the evolution of the disease. Although the Belief Propagation provides exact results on trees, it turns out that is still a good approximation on general graphs. In this cases Belief Propagation may present convergence related issues, especially on dense networks. Moreover, since this approach is based on a very general principle, it can be adapted to study a wide range of issues, some of which I analyze in the thesis