An Improved Mapping and Optimization Method for Implication-based Memristive Circuits Using And-Inverter Graph

Abstract

Any logic operation can be realized in implication-based memristive circuits characterized by low energy consumption and nanometre level size. The synthesis method transforms And-Inverter Graphs (AIGs) representation for logic functions into implication-based networks. It includes a mapping process which converts a cascade of nodes in AIGs to a series of implication gates and detects fan-out nodes simultaneously. An optimized copy process is employed to reduce the delay and area of memristive circuits in occurrence of a fanout node. Experiments are carried out over a benchmark set including 33 functions with input variables from 3 to 41. Experimental results are compared with that from the original algorithm and another Majority-Inverter Graphs (MIG) based mapping method. It shows that the improved algorithm can obtain better performance in latency and area on most of the functions in the test set.

Devising a method of figurative transformations for minimizing boolean functions in the implicative basis

“…Any logical operation can be implemented in the implicative memristor schemes characterized by low energy consumption and the size at the nanometer level. Paper [8] reports a method for converting And-Inverter Graphs (AIGs) for logical functions in the network based on implication. The optimized copying process is used to reduce the latency and area of memory chains.…”

“…The literary sources considered above [4][5][6][7][8][9][10][11][12][13] represent the implementation of the fourth basic element of scheme equipment -the memristor, which is an addition to the resistor, capacitor, and inductiveness.…”

“…All definitions for the logic algebra functions in the {I, OR, NOT} basis have their analogs for the implicative basis { → , NOT} (Table 4). Replacing the basis {I, OR, NOT} with the basis { → , NOT} is possible according to formulae (6) to (8).…”

“…The binary equivalent variables accept a unity value if the variable x i other than x 1 is represented in the terms of function ( 8) in direct code. Conversely, the binary equivalent variable takes zero if the variable x i other than x 1 is represented by the inverse code in the terms of function (8). For x 1 in the terms of function (8), the conditions for entering the binary equivalent are opposite.…”

“…Conversely, the binary equivalent variable takes zero if the variable x i other than x 1 is represented by the inverse code in the terms of function (8). For x 1 in the terms of function (8), the conditions for entering the binary equivalent are opposite. The binary equivalent of the variable x 1 takes a unity value if the variable x 1 is represented in the inverse code.…”