Boolean Factorization Using Two-cube Non-kernels
Oh-Hyeong Kwon,Byung Tae Chun +1 more
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This paper presents a new method for a Boolean factorization that is able to identify two-cube nonkernel Boolean pairs from given expression and shows improvements in literal counts over previous other factorization methods.Abstract:
A factorization is a very important part of multi-level logic synthesis. The number of literals in a factored form is an estimate of the complexity of a logic function, and can be translated directly into the number of transistors required for implementation. Factored forms are described as either algebraic or Boolean, according to the trade-off between run-time and optimization. A Boolean factored form contains fewer number of literals than an algebraic factored form. In this paper, we present a new method for a Boolean factorization. The key idea is to identify two-cube nonkernel Boolean pairs from given expression. Experimental results on various benchmark circuits show the improvements in literal counts over previous other factorization methods.read more
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Common Expression Extraction Using Kernel-Kernel pairs
TL;DR: This paper presents a new Boolean extraction technique for logic synthesis that extracts kernel- kernel pairs as well as cokernel-kernel pairs and provides the common sub-expressions for several logic expressions.
Common Expression Extraction Using Two-cube
Quotient Matrices,Oh-Hyeong Kwon +1 more
Abstract: This paper presents a new Boolean extraction technique for logic synthesis. This method first calculates divisor/2-cube quotients, 2-cube quotient pairs, and 2-cube quotient matrices. Then we find candidates, which can be common sub-expressions, from 2-cube quotients and matrices. Next, candidate intersection provides the common sub-expressions for several logic expressions. Experimental results show the improvements in literal counts over the previous methods. Key Words : 2-cube quotient, 2-cube quotient matrix, Boolean extraction * 교신저자 : 권오형(ohkwon@hanseo.ac.kr)접수일 11년 07월 14일 수정일 (1차 11년 07월 27일, 2차 11년 08월 08일) 게재확정일 11년 08월 11일 1. 서론 여러 논리식들에서 존재할 수 있는 공통식을 찾아 전체 논리식을 간략화하는 공통식 추출(extraction) 방법을 제안한다. 공통식 추출 방법은 일반적으로 여러 논리식을 동시에 나누는 제수(divisor)를 찾고, 이 제수를 포함하는 논리식의 일부를 새로운 변수로 치환하여 전체 논리식들을 간략화 한다. 이러한 공통식 산출에 대한 연구는 크게 대수 나눗셈을 적용한 방법과 부울 나눗셈을 적용한 방법으로 구분할 수 있다. Brayton 등은 커널(kernel) 개념을 도입하여 다항 큐브 제수를 찾는 방법과 커널 교집합을 적용하여 공통식을 찾는 방법을 제안하였다[1-3]. Rajski와 Vasudevamurthy는 단항 큐브와 이 단항 큐브의 보수(complement)를 함께 고려하여 공통식을 찾는 방법[4]을 제안하였다. Singh와 Diwan는 변수 치환을 이용한 공통식 산출 방법[5]을 제안하였다. 이상의 방법들은 대수적 나눗셈에 기반을 둔 방법으로 부울 공리인 등멱법칙 (
Journal ArticleDOI
Common Expression Extraction Using Two-cube Quotient Matrices
TL;DR: This method first calculates divisor/2-cube quotients, 2-Cube quotient pairs, and 2- cube quotient matrices, and finds candidates, which can be common sub-expressions, from 2- Cube quotients and matrices.
References
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