Programming Techniques for Reversible Comparison Sorts

Axelsen, Holger Bock; Yokoyama, T.

doi:10.1007/978-3-319-26529-2_22

Cited by 9 publications

(8 citation statements)

References 10 publications

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“…The reader is encouraged to verify the reversibility of the transitions by starting from the two end states labeled = and = moving backwards problem in reversible programming, even for relatively simple algorithms, cf. [9], and we shall see this problem repeatedly below. The RTM module works as follows.…”

Section: Example: How To Program Reversible String Comparisonmentioning

confidence: 97%

On reversible Turing machines and their function universality

Axelsen

Glück

2016

Acta Informatica

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We provide a treatment of the reversible Turing machines (RTMs) under a strict function semantics. Unlike many existing reversible computation models, we distinguish strictly between computing the function λx. f (x) and computing the function λx. (x, f (x)), or other injective embeddings of f . We reinterpret and adapt a number of important foundational reversible computing results under this semantics. Unifying the results in a single model shows that, as expected (and previously claimed), the RTMs are robust and can compute exactly all injective computable functions. Because injectivity entails that the RTMs are not strictly Turing-complete w.r.t. functions, we use an appropriate alternative universality definition, and show how to derive universal RTMs (URTMs) from existing irreversible universal machines. We then proceed to construct a URTM from the ground up. This resulting machine is the first URTM which does not depend on a reversible simulation of an existing universal machine. The new construction has the advantage that the interpretive overhead of the URTM is limited to a (program dependent) constant factor. Another novelty is that the URTM can function as an inverse interpreter at no asymptotic cost. Mathematics Subject Classification 68Q05 · 68Q10 · 03D10Revised and extended version of the conference papers [4,5].

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Section: Example: How To Program Reversible String Comparisonmentioning

confidence: 97%

On reversible Turing machines and their function universality

Axelsen

Glück

2016

Acta Informatica

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“…The useful criteria for the optimality of reversible algorithms are expected to be different from irreversible ones [1][2][3]. We introduce the two criteria for our analysis: M: The use of memory, except for the original input and output.…”

Section: Reversible Searchmentioning

confidence: 99%

“…Before the loop, l is set to 0, u is set to 2 ⌈log 2 n ⌉ . Thus, the range size is expanded from n to the smallest power of 2 that is greater than or equal to n. At line 12 the middle of the range is set to m. Next, to halve the range, the reversible conditional decreases the upper index u if the middle index is out of the range of in[] or the middle m is greater than the given key k; otherwise, it increases the lower index l. 1 Only the else branch in the j (≥ 1) th iteration changes the ⌈log 2 n⌉ − i th bit from the least significant bit from 0 to 1. Therefore, the control is merged at line 19.…”

Section: Reversible Binary Searchmentioning

confidence: 99%

“…Optimization with human insight leads to improved reversible algorithms for reversible simulations in terms of time, space, output garbage, etc., and such optimizations combining some of these measures have been constructed previously (e.g. [1]). A memory management method developed exclusively for reversible computing has also been studied (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Analyzing Trade-offs in Reversible Linear and Binary Search Algorithms

Masuda¹,

Yokoyama²

2019

Preprint

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Reversible algorithms are algorithms in which each step represents a partial injective function; they are useful for performance optimization in reversible systems. In this study, using Janus, a reversible imperative high-level programming language, we have developed reversible linear and binary search algorithms. We have analyzed the non-trivial space-time trade-offs between them, focusing on the memory usage disregarding original inputs and outputs, the size of the output garbage disregarding the original inputs, and the maximum amount of traversal of the input. The programs in this study can easily be adapted to other reversible programming languages. Our analysis reveals that the change of the output data and/or the data structure affects the design of efficient reversible algorithms. For example, the number of input data traversals depends on whether the search has succeeded or failed, while it expectedly never changes in corresponding irreversible linear and binary searches. Our observations indicate the importance of the selection of data structures and what is regarded as the output with the aim of the reversible algorithm design.

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“…Subsequently, a number of reversibilizations have been optimized in terms of garbage size using domain-specific knowledge (e.g. [2,8,23]). From Boolean logic circuits, which implement total functions over finite domains, it is known that one can minimize the garbage needed to reversibilize a circuit to the information-theoretic minimum [20,24].…”

Section: Introductionmentioning

confidence: 99%

Making Programs Reversible with Minimal Extra Data

Glück

Yokoyama²

2022

New Gener. Comput.

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Reversible computing is an unconventional computing paradigm that comes with specific challenges. One of the important questions is the existence of reversible programs with minimal extra output (garbage data). To answer this question for programs that implement partial functions over countable domains, we introduce an order on infinite garbage sets and a notion of minimality. To this end, we present two methods for functions specified by decidable and semi-decidable predicates. Both methods are universal, which means they work for all programs specified by the predicates. They cover Bennett's classic input-erasing reversible computation of injective functions. Hence, any program written in a Turing-complete programming language can be implemented with g-minimal garbage in an r-Turing-complete reversible programming language. This generality comes at the cost of a considerable runtime due to the generate-and-test approach.

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Programming Techniques for Reversible Comparison Sorts

Cited by 9 publications

References 10 publications

On reversible Turing machines and their function universality

On reversible Turing machines and their function universality

Analyzing Trade-offs in Reversible Linear and Binary Search Algorithms

Making Programs Reversible with Minimal Extra Data

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