Recursive Structures: Growing of Fractals and Plants

1992 ◽  
pp. 9-65
Author(s):  
Heinz-Otto Peitgen ◽  
Hartmut Jürgens ◽  
Dietmar Saupe
Keyword(s):  
Recursive Structures

Preliminaries

2017 ◽  
Author(s):  
David J. Lobina
Keyword(s):  
Data Structures ◽  
Production Systems ◽  
Specific Data ◽  
Recursive Functions ◽  
Recursive Solution ◽  
Partial Recursive Functions ◽  
Recursive Structures ◽  
Recursive Data Structures ◽  
Recursive Data ◽  
The Relationship

Recursion, or the capacity of ‘self-reference’, has played a central role within mathematical approaches to understanding the nature of computation, from the general recursive functions of Alonzo Church to the partial recursive functions of Stephen C. Kleene and the production systems of Emil Post. Recursion has also played a significant role in the analysis and running of certain computational processes within computer science (viz., those with self-calls and deferred operations). Yet the relationship between the mathematical and computer versions of recursion is subtle and intricate. A recursively specified algorithm, for example, may well proceed iteratively if time and space constraints permit; but the nature of specific data structures—viz., recursive data structures—will also return a recursive solution as the most optimal process. In other words, the correspondence between recursive structures and recursive processes is not automatic; it needs to be demonstrated on a case-by-case basis.

Erratum: Application of space-time duality to recursive structures

1986 ◽  
Vol 22 (11) ◽  
pp. 619-619
Author(s):  
N. Farahati
Keyword(s):  
Space Time ◽  
Recursive Structures

scholarly journals Optimal Purely Functional Priority Queues

1996 ◽  
Vol 3 (37) ◽  
Author(s):  
Gerth Stølting Brodal ◽  
Chris Okasaki
Keyword(s):  
Data Structure ◽  
Higher Order ◽  
Priority Queues ◽  
Worst Case ◽  
Minimum Element ◽  
Asymptotically Optimal ◽  
Running Time ◽  
Recursive Structures ◽  
Functional Setting

Brodal recently introduced the first implementation of imperative priority queues to support findMin, insert, and meld in O(1) worst-case time, and deleteMin in O(log n) worst-case time. These bounds are asymptotically optimal among all comparison-based priority queues. In this paper, we adapt<br />Brodal's data structure to a purely functional setting. In doing so, we both simplify the data structure and clarify its relationship to the binomial queues of Vuillemin, which support all four operations in O(log n) time. Specifically, we derive our implementation from binomial queues in three steps: first, we reduce the running time of insert to O(1) by eliminating the possibility of cascading links; second, we reduce the running time of findMin to O(1) by adding a global root to hold the minimum element; and finally, we reduce the running time of meld to O(1) by allowing priority queues to contain other<br />priority queues. Each of these steps is expressed using ML-style functors. The last transformation, known as data-structural bootstrapping, is an interesting<br />application of higher-order functors and recursive structures.

scholarly journals Recent advances in Apertium, a free/open-source rule-based machine translation platform for low-resource languages

2021 ◽  
Author(s):  
Tanmai Khanna ◽  
Jonathan N. Washington ◽  
Francis M. Tyers ◽  
Sevilay Bayatlı ◽  
Daniel G. Swanson ◽  
...  
Keyword(s):  
Open Source ◽  
Machine Translation ◽  
Lexical Selection ◽  
Rule Based ◽  
Low Resource ◽  
Language Technology ◽  
Language Data ◽  
Recursive Structures ◽  
Platform Translation ◽  
Free Open Source

AbstractThis paper presents an overview of Apertium, a free and open-source rule-based machine translation platform. Translation in Apertium happens through a pipeline of modular tools, and the platform continues to be improved as more language pairs are added. Several advances have been implemented since the last publication, including some new optional modules: a module that allows rules to process recursive structures at the structural transfer stage, a module that deals with contiguous and discontiguous multi-word expressions, and a module that resolves anaphora to aid translation. Also highlighted is the hybridisation of Apertium through statistical modules that augment the pipeline, and statistical methods that augment existing modules. This includes morphological disambiguation, weighted structural transfer, and lexical selection modules that learn from limited data. The paper also discusses how a platform like Apertium can be a critical part of access to language technology for so-called low-resource languages, which might be ignored or deemed unapproachable by popular corpus-based translation technologies. Finally, the paper presents some of the released and unreleased language pairs, concluding with a brief look at some supplementary Apertium tools that prove valuable to users as well as language developers. All Apertium-related code, including language data, is free/open-source and available at https://github.com/apertium.

scholarly journals Speech Acts

2016 ◽  
Author(s):  
Stephen C. Levinson
Keyword(s):  
Conversation Analysis ◽  
Speech Acts ◽  
Language Use ◽  
Speech Act ◽  
Linguistic Pragmatics ◽  
Recursive Structures ◽  
Core Language ◽  
Core Issues ◽  
Essential Insight

The essential insight of speech act theory was that when we use language, we perform actions—in a more modern parlance, core language use in interaction is a form of joint action. Over the last thirty years, speech acts have been relatively neglected in linguistic pragmatics, although important work has been done especially in conversation analysis. Here we review the core issues—the identifying characteristics, the degree of universality, the problem of multiple functions, and the puzzle of speech act recognition. Special attention is drawn to the role of conversation structure, probabilistic linguistic cues, and plan or sequence inference in speech act recognition, and to the centrality of deep recursive structures in sequences of speech acts in conversation.

Introduction: Toward an Experimental Lexicography

2020 ◽  
pp. 1-32
Author(s):  
Craig Dworkin
Keyword(s):  
Emily Dickinson ◽  
Jack Kerouac ◽  
Stephane Mallarme ◽  
Reading Practice ◽  
Marcel Duchamp ◽  
Lyn Hejinian ◽  
Recursive Structures ◽  
Conceptual Writing

The introduction summarizes the scope of the project and its methodologies, arguing for a critically descriptive reading practice. Looking at artists’ books, conceptual writing projects, and texts by writers as diverse as Marcel Duchamp, Solmaz Sharif, and Angelo V. Suárez, the chapter first sketches the range of works that engage the dictionary in ways other than those investigated in subsequent chapters. In contrast to writers who have turned to the dictionary as an idealized abstraction, or a source of suppressed cultural biases, the chapter then proposes a dictionary poetics extrapolated from the particular form of reference books and the typography of particular editions, with their emphasis on the chain of the signifier, the chance proximities of otherwise unrelated words, and recursive structures of motivated paths and self-referential loops. Discussing poems by Emily Dickinson, Cecil Giscombe, Lyn Hejinian, Jack Kerouac, and Stéphane Mallarmé the chapter outlines the principles of a radical lexicography in which the inherent logic of the dictionary serves as a generative, structuring device (and not merely an authoritative compendium).

Recursive Structures for the Tree Amplitudes of Multiple Gauge Groups

2008 ◽  
Vol 53 (9(2)) ◽  
pp. 1232-1236
Author(s):  
Jaemo Park ◽  
Woojoo Sim
Keyword(s):  
Gauge Groups ◽  
Recursive Structures
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