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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Using Tree Automata and Regular Expressions to Manipulate...
Nikita Schmidt, Ahmed Patel · 2002-01-12 · via cs.DS updates on arXiv.org

Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to take account of this structuring, which assigns different semantics to different data elements or records. Big variety of structural schemata in use today often requires much flexibility from applications--for example, to process information coming from different sources. To ensure application interoperability, translators are needed that can convert one structure into another. This paper puts forward a formal data model aimed at supporting hierarchical data processing in a simple and flexible way. The model is based on and extends results of two classical theories, studying finite string and tree automata. The concept of finite automata and regular languages is applied to the case of arbitrarily structured tree-like hierarchical data records, represented as "structured strings." These automata are compared with classical string and tree automata; the model is shown to be a superset of the classical models. Regular grammars and expressions over structured strings are introduced. Regular expression matching and substitution has been widely used for efficient unstructured text processing; the model described here brings the power of this proven technique to applications that deal with information trees. A simple generic alternative is offered to replace today's specialised ad-hoc approaches. The model unifies structural and content transformations, providing applications with a single data type. An example scenario of how to build applications based on this theory is discussed. Further research directions are outlined.