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Graphical Method of Reversible Circuits Synthesis

Skorupski A.

International Journal of Electronics and Telecommunications

2017

Vol. 63, No. 3

235--240

This paper presents a new approach to designing reversible circuits. Reversible circuits can decrease energy dissipation theoretically to zero. This feature is a base to build quantum computers. The main problem of reversible logic is designing optimal reversible circuits i.e. circuits with minimal gates number implementing the given reversible function. There are many types of reversible gates. Most popular library is a set of three types of gates so called CNT (Control, NOT and Toffoli). The method presented in this paper is based only on the Toffoli gates. A graphical representation of the reversible function called s-maps is introduced in the paper. This representation allows to find optimal reversible circuits. The paper is organized as follows. Section 1 recalls basic concepts of reversible logic. In Section 2 a graphical representation of the reversible functions is presented. Section 3 describes the algorithm whereby all optimal solutions of the given function could be obtained.

Algorytm syntezy kombinacyjnych układów odwracalnych

Skorupski A., Szyprowski M., Kerntopf P.

Pomiary Automatyka Kontrola

2011

R. 57, nr 8

858-860

W pracy przedstawiono koncepcję nowego algorytmu syntezy układów odwracalnych. Jest on oparty na oryginalnej reprezentacji zamiany wierszy w tablicy prawdy. Dla układów o trzech wejściach i trzech wyjściach sformułowano kryteria takiego doboru bramek, aby otrzymać układ zbliżony do optymalnego. Następnie podano przykład zastosowania przedstawionego algorytmu do syntezy układów o trzech wejściach i trzech wyjściach z bramek Toffoliego.

A gate or circuit is reversible if there is one-to-one correspondence between its input signals and output signals, i.e. if they implement bijective functions. Research on reversible logic circuits is motivated by advances in quantum computing, nanotechnology and low-power design. Recently, the attention has been focused on the synthesis of reversible circuits built from the NCT library of gates consisting of NOT, CNOT and Toffoli gates. This paper presents a novel algorithm for synthesis of reversible circuits. It is based on a new representation of row exchanges in the truth table. There is described how each possible row exchange determines the set of subsequent gates in a circuit, basing on the newly introduced cube of row exchanges. Next, the criteria for the choice of NCT reversible gates are formulated. For an exemplary function, the presented algorithm generates an optimal reversible circuit with 3 inputs and 3 outputs. It can also be generalized to any number of inputs and outputs.