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Programming with “Big Code” Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Programming Techniques for Reversible Comparison Sorts

Authors : Holger Bock Axelsen, Tetsuo Yokoyama

Published in: Programming Languages and Systems

Publisher: Springer International Publishing

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Abstract

A common approach to reversible programming is to reversibly simulate an irreversible program with the desired functionality, which in general puts additional pressure on the computational resources (time, space.) If the same running time is required, ensuring a minimal space overhead is a significant programming challenge.
We introduce criteria for the optimality of reversible simulation: A reversible simulation is faithful if it incurs no asymptotic time overhead and bounds the space overhead (the garbage) by some function g(n), and hygienic if g is (asymptotically) optimal for faithful simulation.
We demonstrate the programming techniques used to develop faithful and hygienic reversible simulations of several well-known comparison sorts, e.g. insertion sort and quicksort, using representations of permutations in both the output and intermediate additional space required.

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previous chapter Objects in Polynomial Time
next chapter Transactions on Mergeable Objects
Appendix
Available only for authorised users
Footnotes
1
This bound can depend significantly on the data structures used. For list sorting, which returns a redundant representation of the sorted array, no garbage is needed.
 
2
If i=n holds at line 9, the loop terminates without evaluating expression https://static-content.springer.com/image/chp%3A10.1007%2F978-3-319-26529-2_22/393248_1_En_22_IEq111_HTML.gif with the out-of-bounds index n, by using short-circuit evaluation.
 
3
The non-variable actual argument n-1 is syntactic sugar for a fresh variable allocated with value \(n-1\) before the call, and deallocated with value \(n-1\) afterwards.
 
4
We remark that Hall’s instruction set is only reversible when programmer discipline is employed, and in fact contains a number of irreversible instructions.
 
5
The size of the auxiliary arrays in merge is not optimized, in order to make the indexing clearer in the presentation.
 
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Axelsen, H.B., Thomsen, M.K.: Garbage-free reversible integer multiplication with constants of the form 2\(^{k}\pm \)2\(^l\pm \)1. In: Glück, R., Yokoyama, T. (eds.) RC 2012. LNCS, vol. 7581, pp. 171–182. Springer, Heidelberg (2013)CrossRef
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Hall, J.S.: A reversible instruction set architecture and algorithms. In: Proceedings of Physics and Computation, pp. 128–134. IEEE Press, New York (1994)
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Yokoyama, T., Axelsen, H.B., Glück, R.: Minimizing garbage size by generating reversible simulations. In: Proceedings of Networking and Computing, pp. 379–387. IEEE Press, New York (2012)
Metadata
Title
Programming Techniques for Reversible Comparison Sorts
Authors
Holger Bock Axelsen
Tetsuo Yokoyama
Copyright Year
2015
Book
Programming Languages and Systems

Print ISBN: 978-3-319-26528-5

Electronic ISBN: 978-3-319-26529-2

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-26529-2_22

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