33,976 research outputs found
Balanced Binary Tree Schemes for Computing Zernike Radial Polynomials
Zernike radial polynomials play a significant role in application areas such
as optics design, imaging systems, and image processing systems. Currently,
there are two kinds of numerical schemes for computing the Zernike radial
polynomials automatically with computer programs: one is based on the
definition in which the factorial operations may lead to the overflow problem
and the high order derivatives are troublesome, and the other is based on
recursion which is either unstable or with high computational complexity. In
this paper, our emphasis is focused on exploring the balanced binary tree (BBT)
schemes for computing Zernike radial polynomials: firstly we established an
elegant formulae for computation; secondly we proposed the recursive and
iterative algorithms based-on BBT; thirdly we analyzed the computational
complexity of the algorithms rigorously; finally we verified and validated the
performance of BBT schemes by testing the running time. Theoretic analysis
shows that the computational complexity of BBT recursive algorithm and
iterative algorithm are exponential and quadratic respectively, which coincides
with the running time test very well. Experiments show that the time
consumption is about microseconds with different computation
platforms for the BBT iterative algorithm (BBTIA), which is stable and
efficient for realtime applications
A survey of parallel execution strategies for transitive closure and logic programs
An important feature of database technology of the nineties is the use of parallelism for speeding up the execution of complex queries. This technology is being tested in several experimental database architectures and a few commercial systems for conventional select-project-join queries. In particular, hash-based fragmentation is used to distribute data to disks under the control of different processors in order to perform selections and joins in parallel. With the development of new query languages, and in particular with the definition of transitive closure queries and of more general logic programming queries, the new dimension of recursion has been added to query processing. Recursive queries are complex; at the same time, their regular structure is particularly suited for parallel execution, and parallelism may give a high efficiency gain. We survey the approaches to parallel execution of recursive queries that have been presented in the recent literature. We observe that research on parallel execution of recursive queries is separated into two distinct subareas, one focused on the transitive closure of Relational Algebra expressions, the other one focused on optimization of more general Datalog queries. Though the subareas seem radically different because of the approach and formalism used, they have many common features. This is not surprising, because most typical Datalog queries can be solved by means of the transitive closure of simple algebraic expressions. We first analyze the relationship between the transitive closure of expressions in Relational Algebra and Datalog programs. We then review sequential methods for evaluating transitive closure, distinguishing iterative and direct methods. We address the parallelization of these methods, by discussing various forms of parallelization. Data fragmentation plays an important role in obtaining parallel execution; we describe hash-based and semantic fragmentation. Finally, we consider Datalog queries, and present general methods for parallel rule execution; we recognize the similarities between these methods and the methods reviewed previously, when the former are applied to linear Datalog queries. We also provide a quantitative analysis that shows the impact of the initial data distribution on the performance of methods
An Algebraic Framework for Compositional Program Analysis
The purpose of a program analysis is to compute an abstract meaning for a
program which approximates its dynamic behaviour. A compositional program
analysis accomplishes this task with a divide-and-conquer strategy: the meaning
of a program is computed by dividing it into sub-programs, computing their
meaning, and then combining the results. Compositional program analyses are
desirable because they can yield scalable (and easily parallelizable) program
analyses.
This paper presents algebraic framework for designing, implementing, and
proving the correctness of compositional program analyses. A program analysis
in our framework defined by an algebraic structure equipped with sequencing,
choice, and iteration operations. From the analysis design perspective, a
particularly interesting consequence of this is that the meaning of a loop is
computed by applying the iteration operator to the loop body. This style of
compositional loop analysis can yield interesting ways of computing loop
invariants that cannot be defined iteratively. We identify a class of
algorithms, the so-called path-expression algorithms [Tarjan1981,Scholz2007],
which can be used to efficiently implement analyses in our framework. Lastly,
we develop a theory for proving the correctness of an analysis by establishing
an approximation relationship between an algebra defining a concrete semantics
and an algebra defining an analysis.Comment: 15 page
An exercise in transformational programming: Backtracking and Branch-and-Bound
We present a formal derivation of program schemes that are usually called Backtracking programs and Branch-and-Bound programs. The derivation consists of a series of transformation steps, specifically algebraic manipulations, on the initial specification until the desired programs are obtained. The well-known notions of linear recursion and tail recursion are extended, for structures, to elementwise linear recursion and elementwise tail recursion; and a transformation between them is derived too
Algorithm Diversity for Resilient Systems
Diversity can significantly increase the resilience of systems, by reducing
the prevalence of shared vulnerabilities and making vulnerabilities harder to
exploit. Work on software diversity for security typically creates variants of
a program using low-level code transformations. This paper is the first to
study algorithm diversity for resilience. We first describe how a method based
on high-level invariants and systematic incrementalization can be used to
create algorithm variants. Executing multiple variants in parallel and
comparing their outputs provides greater resilience than executing one variant.
To prevent different parallel schedules from causing variants' behaviors to
diverge, we present a synchronized execution algorithm for DistAlgo, an
extension of Python for high-level, precise, executable specifications of
distributed algorithms. We propose static and dynamic metrics for measuring
diversity. An experimental evaluation of algorithm diversity combined with
implementation-level diversity for several sequential algorithms and
distributed algorithms shows the benefits of algorithm diversity
Exploiting loop level parallelism in nonprocedural dataflow programs
Discussed are how loop level parallelism is detected in a nonprocedural dataflow program, and how a procedural program with concurrent loops is scheduled. Also discussed is a program restructuring technique which may be applied to recursive equations so that concurrent loops may be generated for a seemingly iterative computation. A compiler which generates C code for the language described below has been implemented. The scheduling component of the compiler and the restructuring transformation are described
Invariant Synthesis for Incomplete Verification Engines
We propose a framework for synthesizing inductive invariants for incomplete
verification engines, which soundly reduce logical problems in undecidable
theories to decidable theories. Our framework is based on the counter-example
guided inductive synthesis principle (CEGIS) and allows verification engines to
communicate non-provability information to guide invariant synthesis. We show
precisely how the verification engine can compute such non-provability
information and how to build effective learning algorithms when invariants are
expressed as Boolean combinations of a fixed set of predicates. Moreover, we
evaluate our framework in two verification settings, one in which verification
engines need to handle quantified formulas and one in which verification
engines have to reason about heap properties expressed in an expressive but
undecidable separation logic. Our experiments show that our invariant synthesis
framework based on non-provability information can both effectively synthesize
inductive invariants and adequately strengthen contracts across a large suite
of programs
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