Clean Reversible Simulations of Ranking Binary Trees View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2018

AUTHORS

Yuhi Ohkubo , Tetsuo Yokoyama , Chishun Kanayama

ABSTRACT

We propose clean reversible simulations of ranking binary trees and unranking as reversible algorithms for reversible computing systems, which are useful for enumerating and randomly generating binary trees. Algorithms for ranking binary trees and their inverses have been studied since the 1970s. Each of these algorithms can be converted into a reversible simulation by saving all data and control information otherwise lost, and each pair of ranking and unranking reversible programs can be combined to realize a clean reversible simulation by using the Bennett method. However, such a clean reversible simulation requires multiple traversal of the given data and/or intermediate data as well as additional storage proportional to the length of the computation. We show that for Knott’s ranking and unranking algorithms, additional storage usage can be reduced by using the proper assertions of reversible loops in embedded reversible simulations. We also show a clean reversible simulation that involves only one traversal. The running time and memory usage of the proposed clean reversible simulations are asymptotically equivalent to those of the original programs by Knott with intermediate garbage of constant size. In general, the derivation strategy of efficient reversible programs from irreversible ones has not yet been established, and this study can be seen as one of the case studies. All the reversible programs presented in this paper can be run on an interpreter of the reversible programming language Janus. More... »

PAGES

243-267

References to SciGraph publications

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  • 2010. Towards a Design Flow for Reversible Logic in NONE
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  • 2005-06-10. NREVERSAL of fortune — The thermodynamics of garbage collection in MEMORY MANAGEMENT
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  • 2013. Garbageless Reversible Implementation of Integer Linear Transformations in REVERSIBLE COMPUTATION
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  • Book

    TITLE

    Reversibility and Universality

    ISBN

    978-3-319-73215-2
    978-3-319-73216-9

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-73216-9_11

    DOI

    http://dx.doi.org/10.1007/978-3-319-73216-9_11

    DIMENSIONS

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