Expression Tree

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Tahar Kechadi - One of the best experts on this subject based on the ideXlab platform.

  • ICFHR - A Real-Time Recognition System for Handwritten Mathematics: Structural Development
    2010 12th International Conference on Frontiers in Handwriting Recognition, 2010
    Co-Authors: Ray Genoe, Tahar Kechadi
    Abstract:

    This paper describes a scalable structural development process, which is part of a real-time recognition approach for handwritten mathematical input. The incremental development of the Expression Tree is important for real-time recognition, due to the requirement of instantaneous user feedback. Traditional parsing techniques are not suitable for this approach. However, the scalability of a grammar-based approach is appealing and has been incorporated into the structural development technique. The Tree is developed, using the relationships discovered by detailed spatial analysis techniques. Due to the fact that unordered and multi-stroke symbols can affect previous increments of the Expression Tree, the system employs a backtracking technique to revert back to previous states. While this avoids the need to impose symbol ordering constraints on the user and reduces the complexity of relationship discovery, we will describe here how it also simplifies the structural development process.

  • FUZZ-IEEE - On the recognition of online handwritten mathematics using feature-based fuzzy rules and relationship precedence
    2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence), 2008
    Co-Authors: Ray Genoe, Tahar Kechadi
    Abstract:

    This paper describes an online recognition system based on a pen-based interface that can be used to analyse the structure of mathematical Expressions. Some of the topics include a feature-based spatial analysis technique and a procedure for constructing Expressions based on relationship precedence. The algorithm discussed combines symbol recognition, spatial analysis and parsing techniques, to generate an Expression Tree of the given mathematical Expression.

  • A Purely Online Approach to Mathematical Expression Recognition
    2006
    Co-Authors: Ray Genoe, John A. Fitzgerald, Tahar Kechadi
    Abstract:

    In this paper a new approach to handwritten mathematical Expression recognition is presented. The approach is highly original in that the solution, an Expression Tree, is immediately updated whenever the user writes a new stroke. Fuzzy logic is used extensively, in both the symbol recognition and structural analysis phases, which is appropriate given the amount of imprecision and ambiguity present in handwritten mathematics. The approach is highly efficient and encouraging results have been achieved.

  • ACST - Structural analysis of handwritten mathematical Expressions through fuzzy parsing
    2006
    Co-Authors: John A. Fitzgerald, Franz Geiselbrechtinger, Tahar Kechadi
    Abstract:

    Including mathematical Expressions in documents can be a tiresome and difficult process. A recognition system for handwritten mathematical Expressions would greatly simplify the task, enabling users to enter Expressions in an intuitive manner. In this paper a powerful yet efficient approach to handwritten mathematical Expression recognition is presented. Our approach is built upon traditional shift-reduce parsing methods which have linear complexity, thus providing the necessary syntax checking and also the basis for an efficient system. Fuzzy logic is introduced to the basic parsing framework, which is appropriate given the ambiguous nature of symbol identities and spatial relationships in handwritten Expressions. Multiple parses are explored whenever strong ambiguities arise, and the most likely Expression Tree is selected as the result.

  • FUZZ-IEEE - An Online Fuzzy Approach to the Structural Analysis of Handwritten Mathematical Expressions
    2006 IEEE International Conference on Fuzzy Systems, 2006
    Co-Authors: Ray Genoe, John A. Fitzgerald, Tahar Kechadi
    Abstract:

    This paper discusses the importance of the structural analysis of mathematical Expressions and the significance of identifying the spatial relationships between symbols to determine the nature of an Expression. It describes a recognition system based on a pen-based interface that can be used to analyse the structure of a mathematical Expression by identifying these relationships. The solution is represented by an Expression Tree. When a new symbol is added to an Expression, fuzzy rules are used to establish what relationships exist between the new symbol and the existing symbols. Once the best relationship has been identified, the Expression Tree is immediately updated.

Ray Genoe - One of the best experts on this subject based on the ideXlab platform.

  • ICFHR - A Real-Time Recognition System for Handwritten Mathematics: Structural Development
    2010 12th International Conference on Frontiers in Handwriting Recognition, 2010
    Co-Authors: Ray Genoe, Tahar Kechadi
    Abstract:

    This paper describes a scalable structural development process, which is part of a real-time recognition approach for handwritten mathematical input. The incremental development of the Expression Tree is important for real-time recognition, due to the requirement of instantaneous user feedback. Traditional parsing techniques are not suitable for this approach. However, the scalability of a grammar-based approach is appealing and has been incorporated into the structural development technique. The Tree is developed, using the relationships discovered by detailed spatial analysis techniques. Due to the fact that unordered and multi-stroke symbols can affect previous increments of the Expression Tree, the system employs a backtracking technique to revert back to previous states. While this avoids the need to impose symbol ordering constraints on the user and reduces the complexity of relationship discovery, we will describe here how it also simplifies the structural development process.

  • FUZZ-IEEE - On the recognition of online handwritten mathematics using feature-based fuzzy rules and relationship precedence
    2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence), 2008
    Co-Authors: Ray Genoe, Tahar Kechadi
    Abstract:

    This paper describes an online recognition system based on a pen-based interface that can be used to analyse the structure of mathematical Expressions. Some of the topics include a feature-based spatial analysis technique and a procedure for constructing Expressions based on relationship precedence. The algorithm discussed combines symbol recognition, spatial analysis and parsing techniques, to generate an Expression Tree of the given mathematical Expression.

  • A Purely Online Approach to Mathematical Expression Recognition
    2006
    Co-Authors: Ray Genoe, John A. Fitzgerald, Tahar Kechadi
    Abstract:

    In this paper a new approach to handwritten mathematical Expression recognition is presented. The approach is highly original in that the solution, an Expression Tree, is immediately updated whenever the user writes a new stroke. Fuzzy logic is used extensively, in both the symbol recognition and structural analysis phases, which is appropriate given the amount of imprecision and ambiguity present in handwritten mathematics. The approach is highly efficient and encouraging results have been achieved.

  • FUZZ-IEEE - An Online Fuzzy Approach to the Structural Analysis of Handwritten Mathematical Expressions
    2006 IEEE International Conference on Fuzzy Systems, 2006
    Co-Authors: Ray Genoe, John A. Fitzgerald, Tahar Kechadi
    Abstract:

    This paper discusses the importance of the structural analysis of mathematical Expressions and the significance of identifying the spatial relationships between symbols to determine the nature of an Expression. It describes a recognition system based on a pen-based interface that can be used to analyse the structure of a mathematical Expression by identifying these relationships. The solution is represented by an Expression Tree. When a new symbol is added to an Expression, fuzzy rules are used to establish what relationships exist between the new symbol and the existing symbols. Once the best relationship has been identified, the Expression Tree is immediately updated.

P. Sadayappan - One of the best experts on this subject based on the ideXlab platform.

  • Memory-optimal evaluation of Expression Trees involving large objects
    Computer Languages Systems & Structures, 2011
    Co-Authors: Chi-chung Lam, Daniel Cociorva, Gerald Baumgartner, Thomas Rauber, P. Sadayappan
    Abstract:

    The need to evaluate Expression Trees involving large objects arises in scientific computing applications such as electronic structure calculations. Often, the Tree node objects are so large that only a subset of them can fit into memory at a time. This paper addresses the problem of finding an evaluation order of the nodes in a given Expression Tree that uses the least amount of memory. We present an algorithm that finds an optimal evaluation order in @Q(nlog^2n) time for an n-node Expression Tree and prove its correctness. We demonstrate the utility of our algorithm using representative equations from quantum chemistry.

  • HiPC - Memory-Optimal Evaluation of Expression Trees Involving Large Objects
    Lecture Notes in Computer Science, 1999
    Co-Authors: Chi-chung Lam, Daniel Cociorva, Gerald Baumgartner, P. Sadayappan
    Abstract:

    The need to evaluate Expression Trees involving large objects arises in scientific computing applications such as electronic structure calculations. Often, the Tree node objects are very large that only a subset of them can fit in memory at a time. This paper addresses the problem of finding an evaluation order of nodes in a given Expression Tree that uses the least memory. We develop an efficient algorithm that finds an optimal evaluation order in O(n 2) time for an n-node Expression Tree.

Zhao Jianju - One of the best experts on this subject based on the ideXlab platform.

  • Unit check and derivation in Modelica based on Expression Tree
    Computer-Aided Engineering, 2013
    Co-Authors: Zhao Jianju
    Abstract:

    To improve the quality and reliability of the complex models in the unified modeling of multidomain physical system,the unit support modes and the unit conversion and calculation rules in Modelica are introduced,and the implementation scheme for unit check and derivation mechanism is proposed on the basis of Expression Tree traversal.The main factors that affects the efficiency are optimized by analyzing the time complexity of the scheme.The scheme is realized on MWorks and proved to be feasible by a model in the standard library of Modelica.

Andreas Blaszczyk - One of the best experts on this subject based on the ideXlab platform.

  • ICPP - Expression Tree Evaluation by Dynamic Code Generation - Are Accelerators Up for the Task?
    2013 42nd International Conference on Parallel Processing, 2013
    Co-Authors: Thomas Müller, Josef Weidendorfer, Andreas Blaszczyk
    Abstract:

    Dynamic code generation techniques are useful if the benefit of code specialized to values only known at runtime outweighs generation time. Such techniques are increasingly employed for HPC applications to tune their runtime behavior. The simulation software investigated in this paper is a typical example: It spends a significant portion of computing time evaluating symbolic formulas which are set up dynamically from model data. However, any software tuning has to match the hardware. Due to the so-called power wall, HPC systems are increasingly equipped with throughput-oriented accelerator components, to allow for rising performance as known from Top500 history. To best exploit such systems, it is important to understand how well applications map to heterogeneous components. While dynamic code generation can work well for standard multi-core systems, in this paper, we research the benefit of accelerators for this scenario. For our application we show that - while the generated code runs well on the accelerator - the generation itself has serious issues, and much better maps to standard multi-cores. Therefore, we see the need that coming HPC systems still have to be equipped with a significant portion of latency-oriented, thus complex general-purpose hardware.