Regular realization of symmetric functions using reversible logic

Digital Combinational Circuits Design with the Help of Symmetric Functions Considering Heat Dissipation by Each QCA Gate

“…A switching function f(x 1, x 2 ,…………,x n ) is called totally symmetric with respect to the variables x 1 , x 2 , x 3 ,……….,x n , [11]- [18], if it is invariant under any permutation of the variables. Total symmetry can be specified by a set of integers (called a numbers) A = (a i ,…..,a j,……… ,a k ) where A ⊂ (0,1,2,….,n); all the vertices with weight w∈A will appear as true minterms in the function.…”

“…Reversible Quantum Computers (QCs) has drawn the attention of researchers recently as such computers result improvement in speed, reducing cost and space etc [1]- [6], [11]- [18]. Reversible gates and circuits are the main components of Quantum Computer.…”

“…Reversible circuits or gates have the same number of inputs and outputs, also have one-to-one mappings between vectors of inputs and outputs; thus the vector of the input states can be uniquely reconstructed from the vector of the output states. A symmetric function [11]- [18] means a Boolean function invariant to the permutation of any of its input variables. Also every Boolean function can be made symmetric by repeating its input variables.…”

Reversible Circuit Synthesis of Symmetric Functions Using a Simple Regular Structure

“…Accordingly, synthesis methods for such functions have been studied extensively [17][18][19][20][21]. Realizations of symmetric functions by reversible logic gates have been described in [9,22,23]. Picton used Fredkin gates to realize digital summation threshold logic (DSTL) devices [23].…”

“…Picton used Fredkin gates to realize digital summation threshold logic (DSTL) devices [23]. An efficient realization of arbitrary symmetric functions using a Reversible Programmable Gate Array (RPGA) has been proposed in [9,22]. We propose a new approach for designing symmetric functions using an array of Peres gates.…”