scholarly journals Local Driving in Higher-Order Positive Supercompilation via the Omega-theorem

10.29007/t4gz ◽  
2018 ◽  
Author(s):  
Geoff Hamilton ◽  
Morten Heine Sørensen
Keyword(s):  
Program Transformation ◽  
Infinite Sequence ◽  
Lambda Calculus ◽  
Higher Order ◽  
New Technique ◽  
Transformation Technique ◽  
First Order ◽  
Auxiliary Functions ◽  
Order Language ◽  
A New Technique

A program transformation technique should terminate, return efficient output programs and be efficient itself.For positive supercompilation ensuring termination requires memoisation of expressions, and these are subsequently used to determine when to perform generalization and folding. For a first-order language, every infinitesequence of transformation steps must include function unfolding, so it is sufficient to memoise only those expressions immediately prior to a function unfolding step.However, for a higher-order language, it is possible for an expression to have an infinite sequence of transformation steps which do not include function unfolding, so memoisation prior to a function unfolding step is not sufficient by itselfto ensure termination. But memoising additional expressions is expensive during transformation and may lead to less efficient output programs due to auxiliary functions. This additional memoisation may happen explicitly during transformationor implicitly via a pre-processing transformation as outlined in previous work by the first author.We introduce a new technique for local driving in higher-order positive supercompilation which obliviates the need for memoising other expressions than function unfolding steps, thereby improving efficiency of both the transformation and the generated programs. We exploit the fact, due to the second author in the setting of type-free lambda-calculus that every expression with an infinite sequence of transformation steps not involving function unfolding must have somthing like the term Omega = (lambda x. x x) (lambda x . x x) embedded within it in a certain sense. The technique has proven useful on a host of examples.

Two-Dimensional Local Deep-Level Transient Spectroscopy Imaging Using Super-Higher-Order Scanning Nonlinear Dielectric Microscopy

2016 ◽  
Author(s):  
N. Chinone ◽  
Y. Cho ◽  
R. Kosugi ◽  
Y. Tanaka ◽  
S. Harada ◽  
...  
Keyword(s):  
Deep Level Transient Spectroscopy ◽  
Deep Level ◽  
Higher Order ◽  
Trap Density ◽  
New Technique ◽  
Two Dimensional ◽  
Nonlinear Dielectric ◽  
Annealing Conditions ◽  
Transient Spectroscopy ◽  
A New Technique

Abstract A new technique for local deep level transient spectroscopy (DLTS) imaging using super-higher-order scanning nonlinear dielectric microscopy is proposed. Using this technique. SiCVSiC structure samples with different post oxidation annealing conditions were measured. We observed that the local DLTS signal decreases with post oxidation annealing (POA), which agrees with the well-known phenomena that POA reduces trap density. Furthermore, obtained local DLTS images had dark and bright areas, which is considered to show the trap distribution at/near SiCVSiC interface.

FINDING k FARTHEST PAIRS AND k CLOSEST/FARTHEST BICHROMATIC PAIRS FOR POINTS IN THE PLANE

1995 ◽  
Vol 05 (01n02) ◽  
pp. 37-51 ◽  
Author(s):  
NAOKI KATOH ◽  
KAZUO IWANO
Keyword(s):  
Voronoi Diagrams ◽  
Search Space ◽  
Higher Order ◽  
Efficient Algorithms ◽  
New Technique ◽  
Enumeration Problems ◽  
A New Technique ◽  
Geometric Enumeration

We study the problem of enumerating k farthest pairs for n points in the plane and the problem of enumerating k closest/farthest bichromatic pairs of n red and n blue points in the plane. We propose a new technique for geometric enumeration problems which iteratively reduces the search space by a half and provides efficient algorithms. As applications of this technique, we develop algorithms, using higher order Voronoi diagrams, for the above problems, which run in O(min{n2, n log n+k4/3log n/log1/3 k}) time and O(n+k4/3/log1/3 k+k log n) space for general Lp metric with p≠2, and O(min{n2, n log n+k4/3}) time and O(n+k4/3+k log n) space for L2 metric. For the problem of enumerating k closest/farthest bichromatic pairs, we shall also discuss the case where we have different numbers of red and blue points. To the authors’ knowledge, no nontrivial algorithms have been known for these problems and our algorithms are faster than trivial ones when k=o(n3/2).

A NEW TECHNIQUE FOR CLASSIFICATION OF DIGITAL SIGNAL TYPES

2008 ◽  
Vol 17 (05) ◽  
pp. 957-971
Author(s):  
ATAOLLAH EBRAHIMZADEH ◽  
ABOLFAZL RANJBAR ◽  
MEHRDAD ARDEBLILPOUR
Keyword(s):  
High Performance ◽  
Cross Validation ◽  
Digital Signal ◽  
Higher Order ◽  
New Technique ◽  
Communication Signals ◽  
Communication Signal ◽  
A New Technique ◽  
Fold Cross Validation

Classification of the communication signals has seen under increasing demands. In this paper, we present a new technique that identifies a variety of digital communication signal types. This technique utilizes a radial basis function neural network (RBFN) as the classifier. Swarm intelligence, as an evolutionary algorithm, is used to construct RBFN. A combination of the higher-order moments and the higher-order cumulants up to eight are selected as the features of the considered digital signal types. In conjunction with RBFN, we have used k-fold cross-validation to improve the generalization potentiality. Simulation results show that the proposed technique has high performance for classification of different communication signals even at very low signal-to-noise ratios.

scholarly journals A Simple Correctness Proof of the Direct-Style Transformation

2002 ◽  
Vol 9 (2) ◽  
Author(s):  
Lasse R. Nielsen
Keyword(s):  
Program Transformation ◽  
Higher Order ◽  
Correctness Proof ◽  
First Order ◽  
Structural Induction ◽  
Higher Order Functions

We build on Danvy and Nielsen's first-order program transformation into continuation-passing style (CPS) to present a new correctness proof of the converse transformation, i.e., a one-pass transformation from CPS back to direct style. Previously published proofs were based on, e.g., a one-pass higher-order CPS transformation, and were complicated by having to reason about higher-order functions. In contrast, this work is based on a one-pass CPS transformation that is both compositional and first-order, and therefore the proof simply proceeds by structural induction on syntax.

scholarly journals Experiments with ZF Set Theory in HOL and Isabelle

1995 ◽  
Vol 2 (37) ◽  
Author(s):  
Sten Agerholm ◽  
Mike Gordon
Keyword(s):  
Set Theory ◽  
Lambda Calculus ◽  
General Purpose ◽  
Higher Order ◽  
Proof Assistants ◽  
Higher Order Logic ◽  
First Order ◽  
Advantages And Disadvantages ◽  
Theory Versus

Most general purpose proof assistants support versions of<br />typed higher order logic. Experience has shown that these logics are capable<br />of representing most of the mathematical models needed in Computer<br />Science. However, perhaps there exist applications where ZF-style<br />set theory is more natural, or even necessary. Examples may include<br />Scott's classical inverse-limit construction of a model of the untyped lambda-calculus<br /> (D_inf) and the semantics of parts of the Z specification notation.<br /><br />This paper compares the representation and use of ZF set theory within<br />both HOL and Isabelle. The main case study is the construction of D_inf.<br />The advantages and disadvantages of higher-order set theory versus first-order<br />set theory are explored experimentally. This study also provides a<br />comparison of the proof infrastructure of HOL and Isabelle.

Parameterizing higher-order processes on names and processes

2019 ◽  
Vol 53 (3-4) ◽  
pp. 153-206
Author(s):  
Xian Xu
Keyword(s):  
Lambda Calculus ◽  
Higher Order ◽  
The Other ◽  
First Order ◽  
Full Abstraction

Parameterization extends higher-order processes with the capability of abstraction and application (like those in lambda-calculus). As is well-known, this extension is strict, meaning that higher-order processes equipped with parameterization are strictly more expressive than those without parameterization. This paper studies strictly higher-order processes (i.e., no name-passing) with two kinds of parameterization: one on names and the other on processes themselves. We present two main results. One is that in presence of parameterization, higher-order processes can interpret first-order (name-passing) processes in a quite elegant fashion, in contrast to the fact that higher-order processes without parameterization cannot encode first-order processes at all. We present two such encodings and analyze their properties in depth, particularly full abstraction. In the other result, we provide a simpler characterization of the standard context bisimilarity for higher-order processes with parameterization, in terms of the normal bisimilarity that stems from the well-known normal characterization for higher-order calculus. As a spinoff, we show that the bisimulation up-to context technique is sound in the higher-order setting with parameterization.

scholarly journals New Comparison Theorems for the Nth Order Neutral Differential Equations with Delay Inequalities

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 454 ◽  
Author(s):  
Osama Moaaz ◽  
Shigeru Furuichi ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Comparison Theorems ◽  
Differential Inequalities ◽  
Neutral Differential Equations ◽  
First Order ◽  
A New Technique ◽  
Equations With Delay ◽  
Higher Order Differential Equations ◽  
First Order Differential Equations

In this work, we present a new technique for the oscillatory properties of solutions of higher-order differential equations. We set new sufficient criteria for oscillation via comparison with higher-order differential inequalities. Moreover, we use the comparison with first-order differential equations. Finally, we provide an example to illustrate the importance of the results.

Improved mixing rates for infinite measure-preserving systems

2013 ◽  
Vol 35 (2) ◽  
pp. 585-614 ◽  
Author(s):  
DALIA TERHESIU
Keyword(s):  
Dynamical Systems ◽  
Simple Proof ◽  
Renewal Theory ◽  
New Technique ◽  
First Order ◽  
Return Map ◽  
Infinite Measure ◽  
Mixing Rates ◽  
A New Technique ◽  
Invent Math

AbstractIn this work, we introduce a new technique for operator renewal sequences associated with dynamical systems preserving an infinite measure that improves the results on mixing rates obtained by Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure. Invent. Math. 1 (2012), 61–110]. Also, this technique allows us to offer a very simple proof of the key result of Melbourne and Terhesiu that provides first-order asymptotics of operator renewal sequences associated with dynamical systems with infinite measure. Moreover, combining techniques used in this work with techniques used by Melbourne and Terhesiu, we obtain first-order asymptotics of operator renewal sequences under some relaxed assumption on the first return map.

scholarly journals A Note on Identity and Higher Order Quantification

2009 ◽  
Vol 7 ◽  
Author(s):  
Rafal Urbaniak
Keyword(s):  
Higher Order ◽  
Second Order ◽  
Identity Relation ◽  
First Order ◽  
Order Language ◽  
Order Set

It is a commonplace remark that the identity relation, even though not expressible in a first-order language without identity with classical set-theoretic semantics, can be defined in a language without identity, as soon as we admit second-order, set-theoretically interpreted quantifiers binding predicate variables that range over all subsets of the domain. However, there are fairly simple and intuitive higher-order languages with set-theoretic semantics (where the variables range over all subsets of the domain) in which the identity relation is not definable. The point is that the definability of identity in higher-order languages not only depends on what variables range over, but also is sensitive to how predication is construed. This paper is a follow-up to (Urbaniak 2006), where it has been proven that no actual axiomatization of Leśniewski’s Ontology determines the standard semantics for the epsilon connective.

scholarly journals Defunctionalization at Work

2001 ◽  
Vol 8 (23) ◽  
Author(s):  
Olivier Danvy ◽  
Lasse R. Nielsen
Keyword(s):  
Program Transformation ◽  
Higher Order ◽  
Practical Applications ◽  
First Order ◽  
Correctness Proofs

We study practical applications of Reynolds's defunctionalization technique, which is a whole-program transformation from higher-order to first-order functional programs. This study leads us to discover new connections between seemingly unrelated higher-order and first-order specifications and their correctness proofs. We thus perceive defunctionalization both as a springboard and as a bridge: as a springboard for discovering new connections between the first-order world and the higher-order world; and as a bridge for transferring existing results between first-order and higher-order settings.

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