Abstract
We present a method for constructing reversible circuitry for multiplying integers by arbitrary integer constants. The method is based on Mealy machines and gives circuits whose size are (in the worst case) linear in the size of the constant. This makes the method unsuitable for large constants, but gives quite compact circuits for small constants. The circuits use no garbage or ancillary lines.
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Axelsen, H.B., Thomsen, M.K.: Garbage-free integer multiplication by constants. In: Glück, R., Yokoyama, T. (eds.) Reversible Computation. LNCS, vol. 7581, pp. 171–182 (2012)
Burignat, S., Vermeirsch, K., De Vos, A., Thomsen, M.K.: Garbageless reversible implementation of integer linear transformations. In: Glück, R., Yokoyama, T. (eds.) RC 2012. LNCS, vol. 7581, pp. 160–170. Springer, Heidelberg (2013)
De Vos, A.: Reversible Computing. Wiley, Chichester (2010)
Huffman, D.A.: Canonical forms for information-lossless finite-state logical machines. IRE Transactions on Information Theory 5(5), 41–59 (1959)
Mealy, G.H.: A method for synthesizing sequential circuits. Bell System Technical Journal 34(5), 1045–1079 (1955)
Rotenberg, E., Cranch, J., Thomsen, M.K., Axelsen, H.B.: Strength of the reversible, garbage-free 2k ±1 multiplier. In: Reversible Computation 2013 (2013)
Wikipedia. Mealy machine (2012), http://en.wikipedia.org/wiki/Mealy_machine
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Mogensen, T.Æ. (2013). Garbage-Free Reversible Constant Multipliers for Arbitrary Integers. In: Dueck, G.W., Miller, D.M. (eds) Reversible Computation. RC 2013. Lecture Notes in Computer Science, vol 7948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38986-3_7
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DOI: https://doi.org/10.1007/978-3-642-38986-3_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38985-6
Online ISBN: 978-3-642-38986-3
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