Composition of switching lattices for regular and for decomposed functions

Multi-terminal switching lattices are typically exploited for modeling switching nano-crossbar arrays that lead to the design and construction of emerging nanocomputers. Typically, the circuit is represented on a single lattice composed by four-terminal switches. In this paper, we propose a two-layer model in order to further minimize the area of regular functions, such as autosymmetric and D-reducible functions, and of decomposed functions. In particular, we propose a switching lattice optimization method for a special class of \u201cregular\u201d 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 order 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 be inputs to 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. Finally, we propose the application of this particular lattice composition technique, based on connected multiple lattices, to the synthesis on switching lattices of D-reducible Boolean functions, and to the more general framework of lattice synthesis based on logic function decomposition