scholarly journals Pushdown flow analysis with abstract garbage collection

2014 ◽  
Vol 24 (2-3) ◽  
pp. 218-283 ◽  
Author(s):  
J. IAN JOHNSON ◽  
ILYA SERGEY ◽  
CHRISTOPHER EARL ◽  
MATTHEW MIGHT ◽  
DAVID VAN HORN
Keyword(s):  
Garbage Collection ◽  
Flow Analysis ◽  
Approximate Solutions ◽  
Higher Order ◽  
Control Flow ◽  
The Other ◽  
Return Flow ◽  
Dynamic Nature ◽  
Pushdown Analysis ◽  
Better Than

AbstractIn the static analysis of functional programs, pushdown flow analysis and abstract garbage collection push the boundaries of what we can learn about programs statically. This work illuminates and poses solutions to theoretical and practical challenges that stand in the way of combining the power of these techniques. Pushdown flow analysis grants unbounded yet computable polyvariance to the analysis of return-flow in higher-order programs. Abstract garbage collection grants unbounded polyvariance to abstract addresses which become unreachable between invocations of the abstract contexts in which they were created. Pushdown analysis solves the problem of precisely analyzing recursion in higher-order languages; abstract garbage collection is essential in solving the “stickiness” problem. Alone, our benchmarks demonstrate that each method can reduce analysis times and boost precision by orders of magnitude. We combine these methods. The challenge in marrying these techniques is not subtle: computing the reachable control states of a pushdown system relies on limiting access during transition to the top of the stack; abstract garbage collection, on the other hand, needs full access to the entire stack to compute a root set, just as concrete collection does.Conditionalpushdown systems were developed for just such a conundrum, but existing methods are ill-suited for the dynamic nature of garbage collection. We show fully precise and approximate solutions to the feasible paths problem for pushdown garbage-collecting control-flow analysis. Experiments reveal synergistic interplay between garbage collection and pushdown techniques, and the fusion demonstrates “better-than-both-worlds” precision.

scholarly journals Solving Nonstiff Higher-Order Ordinary Differential Equations Using 2-Point Block Method Directly

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Hazizah Mohd Ijam ◽  
Mohamed Suleiman ◽  
Ahmad Fadly Nurullah Rasedee ◽  
Norazak Senu ◽  
Ali Ahmadian ◽  
...  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Difference Method ◽  
Divided Difference ◽  
Approximate Solutions ◽  
Higher Order ◽  
Numerical Results ◽  
The Other ◽  
Block Method ◽  
Better Than

We describe the development of a 2-point block backward difference method (2PBBD) for solving system of nonstiff higher-order ordinary differential equations (ODEs) directly. The method computes the approximate solutions at two points simultaneously within an equidistant block. The integration coefficients that are used in the method are obtained only once at the start of the integration. Numerical results are presented to compare the performances of the method developed with 1-point backward difference method (1PBD) and 2-point block divided difference method (2PBDD). The result indicated that, for finer step sizes, this method performs better than the other two methods, that is, 1PBD and 2PBDD.

scholarly journals Exploiting reachability and cardinality in higher-order flow analysis

2008 ◽  
Vol 18 (5-6) ◽  
pp. 821-864 ◽  
Author(s):  
MATTHEW MIGHT ◽  
OLIN SHIVERS
Keyword(s):  
Abstract Interpretation ◽  
Garbage Collection ◽  
Flow Analysis ◽  
Higher Order ◽  
Order Flow ◽  
Environment Analysis ◽  
Running Time

AbstractWe present two complementary improvements for abstract-interpretation-based flow analysis of higher-order languages: (1) abstract garbage collection and (2) abstract counting. Abstract garbage collection is an analog to its concrete counterpart: the analysis determines when an abstract resource has become unreachable, and then, re-allocates it as fresh. This prevents flow sets from joining during abstract interpretation, which has two immediate effects: (1) the precision of the interpretation increases and (2) its running time often falls. In abstract counting, the analysis tracks how many times an abstract resource has been allocated. A count of one implies that the abstract resource momentarily represents only one concrete resource. This knowledge, in turn, drives environment analysis, expanding the kind (rather than just the degree) of optimization available to the compiler.

scholarly journals Systematic abstraction of abstract machines

2012 ◽  
Vol 22 (4-5) ◽  
pp. 705-746 ◽  
Author(s):  
DAVID VAN HORN ◽  
MATTHEW MIGHT
Keyword(s):  
Programming Languages ◽  
Static Analysis ◽  
Abstract Interpretation ◽  
Garbage Collection ◽  
Higher Order ◽  
Return Flow ◽  
Initial Development ◽  
Abstract Machines ◽  
Temporal Ordering

AbstractWe describe a derivational approach to abstract interpretation that yields novel and transparently sound static analyses when applied to well-established abstract machines for higher-order and imperative programming languages. To demonstrate the technique and support our claim, we transform the CEK machine of Felleisen and Friedman (Proc. of the 14th ACM SIGACT-SIGPLAN Symp. Prin. Program. Langs, 1987, pp. 314–325), a lazy variant of Krivine's machine (Higher-Order Symb. Comput. Vol 20, 2007, pp. 199–207), and the stack-inspecting CM machine of Clements and Felleisen (ACM Trans. Program. Lang. Syst. Vol 26, 2004, pp. 1029–1052) into abstract interpretations of themselves. The resulting analyses bound temporal ordering of program events; predict return-flow and stack-inspection behavior; and approximate the flow and evaluation of by-need parameters. For all of these machines, we find that a series of well-known concrete machine refactorings, plus a technique of store-allocated continuations, leads to machines that abstract into static analyses simply by bounding their stores. These machines are parameterized by allocation functions that tune performance and precision and substantially expand the space of analyses that this framework can represent. We demonstrate that the technique scales up uniformly to allow static analysis of realistic language features, including tail calls, conditionals, mutation, exceptions, first-class continuations, and even garbage collection. In order to close the gap between formalism and implementation, we provide translations of the mathematics as running Haskell code for the initial development of our method.

Analytical study of the vibrating double-sided quintic nonlinear nano-torsional actuator using higher-order Hamiltonian approach

2021 ◽  
pp. 146134842110320
Author(s):  
Gamal Mohamed Ismail ◽  
Mahmoud Abul-Ez ◽  
Hijaz Ahmad ◽  
Nadia Mohamed Farea
Keyword(s):  
Analytical Study ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Higher Order ◽  
Second Order ◽  
Hamiltonian Approach ◽  
Homotopy Perturbation ◽  
The Relationship ◽  
Better Than

In this work, we investigate and apply higher-order Hamiltonian approach (HA) as one of the novelty techniques to find out the approximate analytical solution for vibrating double-sided quintic nonlinear nano-torsional actuator. Periodic solutions are analytically verified, and consequently, the relationship between the initial amplitude and the natural frequency are obtained in a novel analytical way. The HA is then extended to the second-order to find more accurate results. To show the accuracy and applicability of the technique, the approximated results are compared with the homotopy perturbation method and numerical solution. According to the numerical results, it is highly remarkable that the second-order approximate solutions produce better than previously existing results and almost similar in comparing with the numerical solutions.

scholarly journals Liberate Abstract Garbage Collection from the Stack by Decomposing the Heap

2020 ◽  
pp. 197-223
Author(s):  
Kimball Germane ◽  
Michael D. Adams
Keyword(s):  
Full Advantage ◽  
Garbage Collection ◽  
Flow Analysis ◽  
Control Flow ◽  
Programming Patterns ◽  
Control Flow Analysis

AbstractAbstract garbage collection and the use of pushdown systems each enhance the precision of control-flow analysis (CFA). However, their respective needs conflict: abstract garbage collection requires the stack but pushdown systems obscure it. Though several existing techniques address this conflict, none take full advantage of the underlying interplay. In this paper, we dissolve this conflict with a technique which exploits the precision of pushdown systems to decompose the heap across the continuation.This technique liberates abstract garbage collection from the stack, increasing its effectiveness and the compositionality of its host analysis. We generalize our approach to apply compositional treatment to abstract timestamps which induces the context abstraction of m-CFA, an abstraction more precise than k-CFA’s for many common programming patterns.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

MUNDANE MIRACLES IN AWADH. ENCOUNTERS WITH THE REVEALED AND THE HIDDEN

2020 ◽  
pp. 130-140
Author(s):  
Maxim B. Demchenko ◽  
Keyword(s):  
The Other ◽  
Local People ◽  
Natural Phenomena ◽  
Mughal Empire ◽  
The Public ◽  
British Raj ◽  
The Subject ◽  
Other World ◽  
Better Than

The sphere of the unknown, supernatural and miraculous is one of the most popular subjects for everyday discussions in Ayodhya – the last of the provinces of the Mughal Empire, which entered the British Raj in 1859, and in the distant past – the space of many legendary and mythological events. Mostly they concern encounters with inhabitants of the “other world” – spirits, ghosts, jinns as well as miraculous healings following magic rituals or meetings with the so-called saints of different religions (Hindu sadhus, Sufi dervishes),with incomprehensible and frightening natural phenomena. According to the author’s observations ideas of the unknown in Avadh are codified and structured in Avadh better than in other parts of India. Local people can clearly define if they witness a bhut or a jinn and whether the disease is caused by some witchcraft or other reasons. Perhaps that is due to the presence in the holy town of a persistent tradition of katha, the public presentation of plots from the Ramayana epic in both the narrative and poetic as well as performative forms. But are the events and phenomena in question a miracle for the Avadhvasis, residents of Ayodhya and its environs, or are they so commonplace that they do not surprise or fascinate? That exactly is the subject of the essay, written on the basis of materials collected by the author in Ayodhya during the period of 2010 – 2019. The author would like to express his appreciation to Mr. Alok Sharma (Faizabad) for his advice and cooperation.

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