2017 Euromicro Conference on Digital System Design (DSD) (2017)

Vienna, Austria

Aug. 30, 2017 to Sept. 1, 2017

ISBN: 978-1-5386-2146-2

pp: 137-144

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/DSD.2017.54

ABSTRACT

Multi-terminal switching lattices are typically exploited for modeling switching nano-crossbar arrays that lead to the design and construction of emerging nanocomputers. In this paper we propose a switching lattice optimization method for a special class of “regular” Boolean functions, called autosymmetric functions. Autosymmetry is a property that is frequent enough within Boolean functions to be interesting in the synthesis process. Each autosymmetric function can be synthesized through a new function (called restriction), depending on less variables and with a smaller on-set, which can be computed in polynomial time. In this paper we describe how to exploit the autosymmetry property of a Boolean function in oder to obtain a smaller lattice representation in a reduced minimization time. The original Boolean function can be constructed through a composition of the restriction with some EXORs of subsets of the input variables. Similarly, the lattice implementation of the function can be constructed using some external lattices for the EXORs, whose outputs will input the lattice implementing the restriction. Finally, the output of the restriction lattice corresponds to the output of the original function. Experimental results show that the total area of the obtained lattices is often significantly reduced. Moreover, in many cases, the computational time necessary to minimize the restriction is smaller than the time necessary to perform the lattice synthesis of the entire function.

INDEX TERMS

Lattices, Boolean functions, Switches, Minimization, Standards, Mathematical model, Nanoscale devices

CITATION

A. Bernasconi, V. Ciriani, L. Frontini and G. Trucco, "Composition of Switching Lattices and Autosymmetric Boolean Function Synthesis,"

*2017 Euromicro Conference on Digital System Design (DSD)*, Vienna, Austria, 2017, pp. 137-144.

doi:10.1109/DSD.2017.54

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