scholarly journals Extensional and Intensional Semantics of Bounded and Unbounded Nondeterminism

2021 ◽  
Vol Volume 17, Issue 4 ◽  
Author(s):  
James Laird

We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which compute them. A fundamental result establishes that these extensional and intensional representations are equivalent, by showing how to construct the unique sequential algorithm which computes a given monotone and stable function, and describing the conditions on sequential algorithms which correspond to continuity with respect to each order. We illustrate by defining may-testing and must-testing denotational semantics for sequential functional languages with bounded and unbounded choice operators. We prove that these are computationally adequate, despite the non-continuity of the must-testing semantics of unbounded nondeterminism. In the bounded case, we prove that our continuous models are fully abstract with respect to may-testing and must-testing by identifying a simple universal type, which may also form the basis for models of the untyped {\lambda}-calculus. In the unbounded case we observe that our model contains computable functions which are not denoted by terms, by identifying a further "weak continuity" property of the definable elements, and use this to establish that it is not fully abstract.

1999 ◽  
Vol 9 (2) ◽  
pp. 191-223 ◽  
Author(s):  
OLAF MÜLLER ◽  
TOBIAS NIPKOW ◽  
DAVID VON OHEIMB ◽  
OSCAR SLOTOSCH

HOLCF is the definitional extension of Church's Higher-Order Logic with Scott's Logic for Computable Functions that has been implemented in the theorem prover Isabelle. This results in a flexible setup for reasoning about functional programs. HOLCF supports standard domain theory (in particular fixpoint reasoning and recursive domain equations), but also coinductive arguments about lazy datatypes. This paper describes in detail how domain theory is embedded in HOL, and presents applications from functional programming, concurrency and denotational semantics.


2021 ◽  
Vol 11 (4) ◽  
pp. 1487
Author(s):  
Yong Jun Jin ◽  
Won Man Park

Extragraft bone formation is crucial for obtaining a successful outcome after spinal fusion surgery. However, the cause of bone formation is not well investigated. In this study, it was hypothesised that extragraft bone formation is generated by mechanical stimuli. A preoperative plan for anterior cervical discectomy and fusion was applied to the finite element model of the C5–C6 motion segment. Extragraft bone formations posterior to the interbody cage were simulated using simultaneous and sequential algorithms. While the simultaneous algorithm predicted the formation of extragraft bone bridging under flexion and extension, the bridge was generated only under extension with the sequential algorithm. This was caused by an ill-defined design space in cases where the simultaneous algorithm was used. Our results using the sequential algorithm show how the progress of extragraft bone formation affects spine mechanics, and our results support the hypothesis that a mechanical stimulus is a major factor influencing extragraft bone formation.


2021 ◽  
Vol 17 (2) ◽  
pp. 145-158
Author(s):  
Ahmad Qawasmeh ◽  
Salah Taamneh ◽  
Ashraf H. Aljammal ◽  
Nabhan Hamadneh ◽  
Mustafa Banikhalaf ◽  
...  

Different high performance techniques, such as profiling, tracing, and instrumentation, have been used to tune and enhance the performance of parallel applications. However, these techniques do not show how to explore the potential of parallelism in a given application. Animating and visualizing the execution process of a sequential algorithm provide a thorough understanding of its usage and functionality. In this work, an interactive web-based educational animation tool was developed to assist users in analyzing sequential algorithms to detect parallel regions regardless of the used parallel programming model. The tool simplifies algorithms’ learning, and helps students to analyze programs efficiently. Our statistical t-test study on a sample of students showed a significant improvement in their perception of the mechanism and parallelism of applications and an increase in their willingness to learn algorithms and parallel programming.


1992 ◽  
Vol 02 (02) ◽  
pp. 113-139
Author(s):  
ARNOB ROY ◽  
JITENDER DEOGUN ◽  
NAVEED A. SHERWANI

Single Row Routing problem is one of the important subproblems in the layout design of multilayer printed circuit boards. This routing technique has also been applied to routing of microwave citcuits and other routing problems. The single row routing problem has been extensively studied and several sequential algorithms have been proposed. In this paper, we present a parallel hypercube algorithm for the single row routing problem. The basis of this parallel algorithm is a new O(n2 log n) sequential algorithm based on the concept of modified cut numbers and a graph decomposition scheme. The sequential algorithm is based on generalizing the concepts underlying two existing sequential algorithms. A parallel algorithm for the hypercube architecture with N processors is then developed by combining the nice features of the sequential algorithm with an efficient allocation scheme. This results in a parallel algorithm of [Formula: see text] complexity. The experimental results show that our algorithm achieves a speed up factor that is quite close to the theoretical bound while maintaining the quality of the solutions, as compared to any existing sequential algorithm. Moreover, the algorithm produces 28% better results than any existing results.


1991 ◽  
Author(s):  
Joseph P. Magliano ◽  
Robert Cohen ◽  
Gary L. Allen ◽  
James R. Rodrigue

Author(s):  
Benson Farb ◽  
Dan Margalit

This chapter explains and proves the Nielsen–Thurston classification of elements of Mod(S), one of the central theorems in the study of mapping class groups. It first considers the classification of elements for the torus of Mod(T² before discussing higher-genus analogues for each of the three types of elements of Mod(T². It then states the Nielsen–Thurston classification theorem in various forms, as well as a connection to 3-manifold theory, along with Thurston's geometric classification of mapping torus. The rest of the chapter is devoted to Bers' proof of the Nielsen–Thurston classification. The collar lemma is highlighted as a new ingredient, as it is also a fundamental result in the hyperbolic geometry of surfaces.


2015 ◽  
Vol 5 (1) ◽  
pp. 606-620
Author(s):  
Mahtali Sbih ◽  
Zoubeir BENSID ◽  
Zohra BOUNOUARA ◽  
Fouad DJAIZ ◽  
Youcef FERRAG

The goal of fertilization is to meet the nutritional needs of plants by completing the supply of soil nutrients in an economically profitable and environmentally friendly. Achieving on-farm optimum economic crop yields of marketable quality with minimum adverse environmental impact requires close attention to fertilization guide. The recommendations seek to do this by ensuring that the available supply of plant nutrients in soil is judiciously supplemented by additions of nutrients in fertilizers. The objective is that crops must have an adequate supply of nutrients, and many crops show large and very profitable increases in yield from the correct use of fertilizers to supply nutrients. The main objective of this work is to establishing a reference guide of fertilization of vegetable crops and cereal in Algeria. To meet this objective, we have processes in two steps: 1) Establishment of theoretical fertilizer recommendation from international guide of crop fertilization; 2) Validation of these developed theoretical fertilizer recommendation by trials in the fields. Sixteen fertilization guides of vegetable crops from the Canadian provinces (5 guides), USA (10 guides) and countries of northern Europe England (1 guide). Generally, the rating of these recommendation is ranging from poor soil to soil exceedingly rich; however, the numbers of fertility classes are very different. Indeed, Quebec Ontario, Minnesota, Wisconsin New England, Maryland and Kentucky and Florida guides are subdivided into 5 fertility classes, ranging from poor soil to soil exceedingly rich. The recommendation of New Brunswick and Manitoba contain six classes. The recommendation of Michigan, Nova Scotia and England contain 10 and 7 fertility classes respectively. The recommendation fertilizer of New York and New Jersey have 3classes. Unlike the systems of fertilization recommendation mentioned above, the recommendation fertilizer of Pennsylvania is based on continuous models of P, K and contains 34 classes for P and 22 classes K. Then we standardized the P soil analysis with conversion equations (Olsen method) and units of measurement (kg/ha, mg/kg…).Following this procedure we transformed discontinued systems of fertility classes in to continuous models to facilitate comparison between the different fertilization recommendation models in one hand, in other hand to obtain critical value (CV).Finally, we used statistics of the conditional expectation in order to generate the theoretical recommendation fertilization guide of fertilization with 7 fertility classes (VL, L, M, MH, OP, H and VH). The next step was calibrating soil tests against yield responses to applied nutrient in field experiments. A database (not published data) from agriculture and agri-food Canada, were used. Production of pumpkin responded positively and significantly to P or K soil fertility levels, increases being observed with P more often than with K. According to the Cate-Nelson methods, the critical value of Olsen-P in the top 20 cm of soil was about 25 mg/kg: at values of greater than or equal to 25 mg/kg, crops achieved about 80% of their maximal yield in the absence of fertilizer application. The CV of K in soil for this crop was about 140 mg/kg. The CV found was very close to this generated by the theoretical method for recommendation of fertilization guide. Finally, we used the procedure of Cope and Rouse in both sides of the CV in order to make subdivisions of different groups of soil fertility. One calibrates the soil-test value against yield response to tile nutrient to predict fertilizer requirement.


2021 ◽  
Vol 26 ◽  
pp. 1-67
Author(s):  
Patrick Dinklage ◽  
Jonas Ellert ◽  
Johannes Fischer ◽  
Florian Kurpicz ◽  
Marvin Löbel

We present new sequential and parallel algorithms for wavelet tree construction based on a new bottom-up technique. This technique makes use of the structure of the wavelet trees—refining the characters represented in a node of the tree with increasing depth—in an opposite way, by first computing the leaves (most refined), and then propagating this information upwards to the root of the tree. We first describe new sequential algorithms, both in RAM and external memory. Based on these results, we adapt these algorithms to parallel computers, where we address both shared memory and distributed memory settings. In practice, all our algorithms outperform previous ones in both time and memory efficiency, because we can compute all auxiliary information solely based on the information we obtained from computing the leaves. Most of our algorithms are also adapted to the wavelet matrix , a variant that is particularly suited for large alphabets.


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