Polarity Optimization Of FPRM Based On XNOR/OR

Optimization of power and area in Integrated Circuit (IC) logic layer which aims at minimization of circuit's power dissipation and area is one important component of modern IC design. Most of the previous studies are based on Boolean logic. In fact, the XOR/AND or XNOR/OR based Reed-Muller (RM) logic has many obvious superiorities over the conventional Boolean logic. As to n-variable logic function of Fixed-Polarity RM (FPRM) logic,2" FPRM expressions are possible, each corresponding to a unique polarity. Obviously, polarity decides the complexity of a RM logic function, and it further affects the circuit power, area and speed. So it is necessary to study the best polarity searching (i.e., polarity optimization) techniques of RM logic circuits under specific objective. The current RM logic synthesis and optimization are mainly focused on XOR/AND circuits, research on XNOR/OR circuits is relatively small. Therefore, this dissertation makes systemic researches on polarity optimization of XNOR/OR based FPRM circuits, with power minimization and area minimization as the objectives. The main contents are as follows:1) Mathematical models of polarity optimization of XNOR/OR circuits:After carefully studying the characteristics of the current polarity evaluation techniques in FPRM circuit polarity optimization, methods on circuit area and power dissipation estimation were coordinated and refined, and on this basis, mathematical models were established in which circuit area minimization, power minimization, circuit area and power integrated optimization were included.2) Polarity optimization algotithms for large-scaled circuits:In order to solve the mathematical models of XNOR/OR circuits, a Simple Parallel Evolution Algorithm (SPEA) was established firstly, by integrating the advantages of the Traditional Genetic Algorithm (TGA) and the Traditional Quantum Algorithm (TQA); To improve the optimum performance of SPEA, an algorithm named Population Co-Evolution Algorithm (PCEA) was proposed by introducing co-evolutionary idea into the SPEA. In order to enhance the optimization performance of niche genetic algorithm in multimodal problems solving, improved niche genetic algorithms were proposed by defining two dynamic adjustment strategies of niche radius. To improve the global optimization ability of the algorithm, a Co-Evolutionary Niche Genetic Algorithm (CENGA) was proposed by introducing co-evolutionary idea into the improved niche genetic algorithm. Simulation results on standard functions verified the optimization performance of the two type algorithms.3) Polarity conversion and polarity traversal strategy:After analyzing several tabular technique based polarity conversion algorithms, a parallel tabular polarity conversion algorithm used between different FPRM polarities was proposed, which integrated the advantages of two of the algorithms analyzed. Simulation results showed that the parallel polarity conversion algorithm had better efficiency compared to its opponents. Intelligent algorithms are usually used in best polarity searching of large-scaled FPRM circuits, in order to speedup the polarity conversion process of each generation and improve efficiency of the whole optimization scheme, a strategy named the Least Operations polarity Traversal Method (LOTM) for incomplete polarity collection was proposed. The LOTM's applicability for XNOR/OR circuits of different scales was analyzed based on simulation results of 12 benchmark circuits.4) Low-power decomposition of multi-input logic gates:Through in-depth analysis of the low-power decomposition problem of multi-input logic gates and the current decomposition techniqes based on classification, the problem was transformed into a smallest binary tree searching problem. Signal probability was used to express the distances between the trees, and an Universal low power Decomposition algorithm for Multi-input Logic Gates (UDMLG), which was based on greedy idea, was proposed. Simulation results on MCNC benchmark circuits verified the algorithm's stability and efficiency.5) Polarity optimization of XNOR/OR circuits with power or area minimization as objective:Based on the above results, polarity optimization schemes of XNOR/OR circuits for low power dissipation and area minimization were constructed in which PCEA was used as best polarity searching algorithm. Based on the CENGA, a multi best polarities searching scheme with the objective of minimizing circuit area was established for XNOR/OR circuits which have more than one best polarity, and based on experimental data on MCNC benchmark circuits, difference of CENGA applicability to multimodal functions and to FPRM circuit polarity optimization was analyzed and the CENGA was modified to improve the optimization of multi best polarity circuits.6) Multi-objective Polarity optimization of XNOR/OR circuits:Aiming at exploring the best polarity distribution characteristics of FPRM circuits with multiple objectives, the multi-objective genetic algorithm was modified according to the feature of XNOR/OR multi-objective polarity optimization, and an integrated optimization scheme based on the modified algorithm was proposed to minimize area and power dissipation of XNOR/OR circuits simultaneously. Characteristics and patterns of polarity distribution of XNOR/OR circuits under multi performance index were analyzed and summarized based on simulation data.