Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

9-2015

Journal or Book Title

Natural Computing

Volume

14

DOI

10.1007/s11047-014-9438-5

Abstract

We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices to encode each logical bit, we obtain universal computation. We also highlight a phenomenon of “back forcing” as a property of each function. Such a phenomenon occurs in a circuit when the input of gates which have been already used at a given time step is further modified by a computation actually performed at a later stage. Finally, we show that zero forcing can be also used to implement reversible computation. The model introduced here provides a potentially new tool in the analysis of Boolean functions, with particular attention to monotonicity. Moreover, in the light of applications of zero forcing in quantum mechanics, the link with Boolean functions may suggest a new directions in quantum control theory and in the study of engineered quantum spin systems. It is an open technical problem to verify whether there is a link between zero forcing and computation with contact circuits.

Comments

This is an article from Natural Computing 14 (2015): 485, doi:10.1007/s11047-014-9438-5. Posted with permission.

Rights

This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Copyright Owner

The Authors

Language

en

File Format

application/pdf

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