Compressed Tree Representations

2016 ◽  
pp. 397-401
Author(s):  
Gonzalo Navarro ◽  
Kunihiko Sadakane
Keyword(s):  
Tree Representations

scholarly journals Isomorphisms between determinantal point processes with translation-invariant kernels and Poisson point processes

2020 ◽  
pp. 1-14
Author(s):  
SHOTA OSADA
Keyword(s):  
Point Processes ◽  
Duke Math ◽  
Random Point ◽  
Determinantal Point Processes ◽  
Fredholm Determinants ◽  
Poisson Point Processes ◽  
Translation Invariant ◽  
Ergodic Properties ◽  
Tree Representations ◽  
Invariant Kernels

Abstract We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulli property was proved by Lyons and Steif [Stationary determinantal processes: phase multiplicity, bernoullicity, and domination. Duke Math. J.120 (2003), 515–575] and Shirai and Takahashi [Random point fields associated with certain Fredholm determinants II: fermion shifts and their ergodic properties. Ann. Probab.31 (2003), 1533–1564]. We prove its continuum version. For this purpose, we also prove the Bernoulli property for the tree representations of the determinantal point processes.

An Algorithm for the Enumeration of Serial and/or Parallel Combinations of Kinematic Building Blocks

2004 ◽  
Author(s):  
Hong-Sen Yan ◽  
Feng-Ming Ou ◽  
Ming-Feng Tang
Keyword(s):  
Graph Theory ◽  
Building Blocks ◽  
Power Source ◽  
Cam Follower ◽  
Tree Representations ◽  
The Given

An algorithm is presented, based on graph theory, for enumerating all feasible serial and/or parallel combined mechanisms from the given rotary or translational power source and specific kinematic building blocks. Through the labeled out-tree representations for the configurations of combined mechanisms, the enumeration procedure is developed by adapting the algorithm for the enumeration of trees. A rotary power source and four kinematic building blocks: a crank-rocker linkage, a rack-pinion, a double-slider mechanism, and a cam-follower mechanism, are chosen as the combination to illustrate the algorithm. And, two examples are provided to validate the algorithm.

scholarly journals Multi-purpose Syntax Definition with SDF3

2020 ◽  
pp. 1-23 ◽  
Author(s):  
Luís Eduardo de Souza Amorim ◽  
Eelco Visser
Keyword(s):  
Error Recovery ◽  
Abstract Syntax ◽  
Abstract Syntax Tree ◽  
Syntax Tree ◽  
Full Class ◽  
High Level ◽  
Modular Composition ◽  
Tree Representations ◽  
Context Free ◽  
Context Free Grammars

Abstract SDF3 is a syntax definition formalism that extends plain context-free grammars with features such as constructor declarations, declarative disambiguation rules, character-level grammars, permissive syntax, layout constraints, formatting templates, placeholder syntax, and modular composition. These features support the multi-purpose interpretation of syntax definitions, including derivation of type schemas for abstract syntax tree representations, scannerless generalized parsing of the full class of context-free grammars, error recovery, layout-sensitive parsing, parenthesization and formatting, and syntactic completion. This paper gives a high level overview of SDF3 by means of examples and provides a guide to the literature for further details.

scholarly journals Associative and commutative tree representations for Boolean functions

2015 ◽  
Vol 570 ◽  
pp. 70-101 ◽  
Author(s):  
Antoine Genitrini ◽  
Bernhard Gittenberger ◽  
Veronika Kraus ◽  
Cécile Mailler
Keyword(s):  
Boolean Functions ◽  
Tree Representations

scholarly journals Graphs of edge-intersecting non-splitting paths in a tree: Representations of holes—Part I

2016 ◽  
Vol 215 ◽  
pp. 47-60 ◽  
Author(s):  
Arman Boyacı ◽  
Tınaz Ekim ◽  
Mordechai Shalom ◽  
Shmuel Zaks
Keyword(s):  
Tree Representations

Analyzing Holistic Parsers: Implications for Robust Parsing and Systematicity

2001 ◽  
Vol 13 (5) ◽  
pp. 1137-1170 ◽  
Author(s):  
Edward Kei Shiu Ho ◽  
Lai Wan Chan
Keyword(s):  
Parse Tree ◽  
State Transitions ◽  
Generalization Performance ◽  
Original Sentence ◽  
Representational Space ◽  
Grammatical Errors ◽  
Robust Parsing ◽  
Input Sentence ◽  
Parse Trees ◽  
Tree Representations

Holistic parsers offer a viable alternative to traditional algorithmic parsers. They have good generalization performance and are robust inherently. In a holistic parser, parsing is achieved by mapping the connectionist representation of the input sentence to the connectionist representation of the target parse tree directly. Little prior knowledge of the underlying parsing mechanism thus needs to be assumed. However, it also makes holistic parsing difficult to understand. In this article, an analysis is presented for studying the operations of the confluent pre-order parser (CPP). In the analysis, the CPP is viewed as a dynamical system, and holistic parsing is perceived as a sequence of state transitions through its state-space. The seemingly one-shot parsing mechanism can thus be elucidated as a step-by-step inference process, with the intermediate parsing decisions being reflected by the states visited during parsing. The study serves two purposes. First, it improves our understanding of how grammatical errors are corrected by the CPP. The occurrence of an error in a sentence will cause the CPP to deviate from the normal track that is followed when the original sentence is parsed. But as the remaining terminals are read, the two trajectories will gradually converge until finally the correct parse tree is produced. Second, it reveals that having systematic parse tree representations alone cannot guarantee good generalization performance in holistic parsing. More important, they need to be distributed in certain useful locations of the representational space. Sentences with similar trailing terminals should have their corresponding parse tree representations mapped to nearby locations in the representational space. The study provides concrete evidence that encoding the linearized parse trees as obtained via preorder traversal can satisfy such a requirement.

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