Data-Structure Rewriting

We tackle the problem of data-structure rewriting including pointer redirections. We propose two basic rewrite steps: (i) Local Redirection and Replacement steps the aim of which is redirecting specific pointers determined by means of a pattern, as well as adding new information to an existing data ; and (ii) Global Redirection steps which are aimed to redirect all pointers targeting a node towards another one. We define these two rewriting steps following the double pushout approach. We define first the category of graphs we consider and then define rewrite rules as pairs of graph homomorphisms of the form "L R". Unfortunately, inverse pushouts (complement pushouts) are not unique in our setting and pushouts do not always exist. Therefore, we define rewriting steps so that a rewrite rule can always be performed once a matching is found

Trajectory Codes for Flash Memory

Flash memory is well-known for its inherent asymmetry: the flash-cell charge levels are easy to increase but are hard to decrease. In a general rewriting model, the stored data changes its value with certain patterns. The patterns of data updates are determined by the data structure and the application, and are independent of the constraints imposed by the storage medium. Thus, an appropriate coding scheme is needed so that the data changes can be updated and stored efficiently under the storage-medium's constraints. In this paper, we define the general rewriting problem using a graph model. It extends many known rewriting models such as floating codes, WOM codes, buffer codes, etc. We present a new rewriting scheme for flash memories, called the trajectory code, for rewriting the stored data as many times as possible without block erasures. We prove that the trajectory code is asymptotically optimal in a wide range of scenarios. We also present randomized rewriting codes optimized for expected performance (given arbitrary rewriting sequences). Our rewriting codes are shown to be asymptotically optimal.Comment: Submitted to IEEE Trans. on Inform. Theor

Rewriting Systems over Nested Data Words

We propose a generic framework for reasoning about infinite state systems handling data like integers, booleans etc. and having complex control structures. We consider that configurations of such systems are represented by nested data words, i.e., words of ... words over a potentially infinite data domain. We define a logic called $ndwl$ allowing to reason about nested data words, and we define rewriting systems called $ndwrs$ over these nested structures. The rewriting systems are constrained by formulas in the logic specifying the rewriting positions as well as structure/data transformations. We define a fragment $Sigma_2^*$ of $ndwl$ with a decidable satisfiability problem. Moreover, we show that the transition relation defined by rewriting systems with $Sigma_2^*$ constraints can be effectively defined in the same fragment. These results can be used in the automatization of verification problems such as inductive invariance checking and bounded reachability analysis. Our framework allows to reason about a wide range of concurrent systems including multithreaded programs (with procedure calls, thread creation, global/local variables over infinite data domains, locks, monitors, etc.), dynamic networks of timed systems, cache coherence/mutex/communication protocols, etc

Structure Pattern Analysis Using Term Rewriting and Clustering Algorithm

Biological data is accumulated at a fast pace. However, raw data are generally difficult to understand and not useful unless we unlock the information hidden in the data. Knowledge/information can be extracted as the patterns or features buried within the data. Thus data mining, aims at uncovering underlying rules, relationships, and patterns in data, has emerged as one of the most exciting fields in computational science. In this dissertation, we develop efficient approaches to the structure pattern analysis of RNA and protein three dimensional structures. The major techniques used in this work include term rewriting and clustering algorithms. Firstly, a new approach is designed to study the interaction of RNA secondary structures motifs using the concept of term rewriting. Secondly, an improved K-means clustering algorithm is proposed to estimate the number of clusters in data. A new distance descriptor is introduced for the appropriate representation of three dimensional structure segments of RNA and protein three dimensional structures. The experimental results show the improvements in the determination of the number of clusters in data, evaluation of RNA structure similarity, RNA structure database search, and better understanding of the protein sequence-structure correspondence

StructRe: Rewriting for Structured Shape Modeling

Man-made 3D shapes are naturally organized in parts and hierarchies; such structures provide important constraints for shape reconstruction and generation. Modeling shape structures is difficult, because there can be multiple hierarchies for a given shape, causing ambiguity, and across different categories the shape structures are correlated with semantics, limiting generalization. We present StructRe, a structure rewriting system, as a novel approach to structured shape modeling. Given a 3D object represented by points and components, StructRe can rewrite it upward into more concise structures, or downward into more detailed structures; by iterating the rewriting process, hierarchies are obtained. Such a localized rewriting process enables probabilistic modeling of ambiguous structures and robust generalization across object categories. We train StructRe on PartNet data and show its generalization to cross-category and multiple object hierarchies, and test its extension to ShapeNet. We also demonstrate the benefits of probabilistic and generalizable structure modeling for shape reconstruction, generation and editing tasks.Comment: Our project page: https://jiepengwang.github.io/StructRe

Magnetic ordering, spin waves, and Haldane gap excitations in (Nd_x Y_{1-x})_2 Ba Ni O_5 linear-chain mixed-spin antiferromagnets

Linear-chain nickelates with the composition (Nd_x Y_{1-x})_2 Ba Ni O_5 (x=1, x=0.75, x=0.5, and x=0.25) are studied in a series of neutron scattering experiments. Powder diffraction is used to determine the temperature dependence of the magnetic structure in all four systems. Single-crystal inelastic neutron scattering is employed to investigate the temperature dependence of the Haldane-gap excitations and low-energy spin waves in the x=1 compound Nd_2 Ba Ni O_5. The results of these experiments are discussed in the context of the ``Haldane chain in a staggered field'' model for R_2 Ba Ni O_5 systems, and quantitative agreement with theory is obtained.Comment: Major rewriting and inclusion of new experimental data 30 pages, 14 figure

Two variants of the froidure-pin algorithm for finite semigroups

In this paper, we present two algorithms based on the Froidure-Pin Algorithm for computing the structure of a finite semigroup from a generating set. As was the case with the original algorithm of Froidure and Pin, the algorithms presented here produce the left and right Cayley graphs, a confluent terminating rewriting system, and a reduced word of the rewriting system for every element of the semigroup. If U is any semigroup, and A is a subset of U, then we denote by the least subsemigroup of U containing A. If B is any other subset of U, then, roughly speaking, the first algorithm we present describes how to use any information about , that has been found using the Froidure-Pin Algorithm, to compute the semigroup . More precisely, we describe the data structure for a finite semigroup S given by Froidure and Pin, and how to obtain such a data structure for from that for . The second algorithm is a lock-free concurrent version of the Froidure-Pin Algorithm.PostprintPeer reviewe

Dynamic Trace-Based Data Dependency Analysis for Parallelization of C Programs

Writing parallel code is traditionally considered a difficult task, even when it is tackled from the beginning of a project. In this paper, we demonstrate an innovative toolset that faces this challenge directly. It provides the software developers with profile data and directs them to possible top-level, pipeline-style parallelization opportunities for an arbitrary sequential C program. This approach is complementary to the methods based on static code analysis and automatic code rewriting and does not impose restrictions on the structure of the sequential code or the parallelization style, even though it is mostly aimed at coarse-grained task-level parallelization. The proposed toolset has been utilized to define parallel code organizations for a number of real-world representative applications and is based on and is provided as free source