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International Conference on Reversible Computation

RC 2016: Reversible Computation pp 322–337Cite as

Checking Reversibility of Boolean Functions

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9720))

Abstract

Following the reversible computation paradigm is essential in the design of many emerging technologies such as quantum computation or dedicated low power concepts. The design of corresponding circuits and systems heavily relies on information about whether the function to be realized is indeed reversible. In particular in hierarchical synthesis approaches where a given function is decomposed into sub-functions, this is often not obvious. In this paper, we prove that checking reversibility of Boolean functions is indeed coNP-complete. Besides that, we propose two complementary approaches which, despite the complexity, can tackle this problem in an efficient fashion. An experimental evaluation shows the feasibility of the approaches.

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Notes

  1. 1.

    Initial experiments verifying the underlying link between information-loss and thermodynamics have been reported in [3].

  2. 2.

    Note that this problem has been recognized in other works concerning embedding (e.g. [21]) and synthesis (e.g. [19]). But, thus far, the issue has only been addressed peripherally and without a theoretical consideration, explicit algorithms, or an experimental evaluation.

  3. 3.

    Since functions \(f:\mathbb {B}^n\rightarrow \mathbb {B}^m\) with \(n\ne m\) are not reversible by definition, we are assuming an equal number n of inputs and outputs in the following.

  4. 4.

    A similar idea has been employed for equivalence checking in the domain of verification (see e.g. [1, 4]). In our context, instead of two different functions, the same function is considered twice and, instead of applying the same pattern on both functions, we apply different patterns.

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Acknowledgments

This work has partially been supported by the EU COST Action IC1405.

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Authors and Affiliations

  1. Institute for Integrated Circuits, Johannes Kepler University, 4040, Linz, Austria

    Robert Wille

  2. Cyber-Physical Systems, DFKI GmbH, 28359, Bremen, Germany

    Robert Wille

  3. Institute of Computer Science, University of Bremen, 28359, Bremen, Germany

    Aaron Lye & Philipp Niemann

Authors
  1. Robert Wille
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  2. Aaron Lye
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  3. Philipp Niemann
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Corresponding author

Correspondence to Robert Wille .

Editor information

Editors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Simon Devitt

  2. University of Bologna/Inria, Bologna, Italy

    Ivan Lanese

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Wille, R., Lye, A., Niemann, P. (2016). Checking Reversibility of Boolean Functions. In: Devitt, S., Lanese, I. (eds) Reversible Computation. RC 2016. Lecture Notes in Computer Science(), vol 9720. Springer, Cham. https://doi.org/10.1007/978-3-319-40578-0_23

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  • DOI: https://doi.org/10.1007/978-3-319-40578-0_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40577-3

  • Online ISBN: 978-3-319-40578-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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