Generalized Inclusive Forms—New Canonical Reed-Muller Forms Including Minimum ESOPs

This paper describes two families of canonical Reed-Muller forms, called inclusive forms (IFs) and their generalization, the generalized inclusive forms (GIFs), which include minimum ESOPs for any Boolean function. We outline the hierarchy of known canonical forms, in particular, pseudo-generalized Kronecker forms (PGKs), which led us to the discovery of the new families. Next, we introduce special binary trees, called the S/D trees, which underlie IFs and permit their enumeration. We show how to generate IFs and GIFs and prove that GIFs include minimum ESOPs. Finally, we present the results of computer experiments, which show that GIFs reduce the search space for minimum ESOP by several orders of magnitude, and this reduction grows exponentially with the number of variables.

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IMPROVING THE EFFICIENCY OF A LEAST MEDIAN OF SQUARES SCHEMA FOR THE ESTIMATION OF THE FUNDAMENTAL MATRIX

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001406004922 ◽

2006 ◽

Vol 20 (05) ◽

pp. 633-648 ◽

Cited By ~ 1

Author(s):

MARIA TRUJILLO ◽

EBROUL IZQUIERDO

Keyword(s):

Fundamental Matrix ◽

Input Data ◽

Selection Process ◽

Computational Cost ◽

Computer Experiments ◽

Search Space ◽

Least Square ◽

Practical Applications ◽

Least Median Of Squares ◽

Low Dimensionality

A robust and efficient approach to estimate the fundamental matrix is proposed. The main goal is to reduce the computational cost involved in the estimation when robust schemas are applied. The backbone of the proposed technique is the conventional Least Median of Squares (LMedS) technique. It is well known that the LMedS is one of the most robust regressors for highly contaminated data and unstable models. Unfortunately, its computational complexity renders it useless for practical applications. To overcome this problem, a small number of low-dimensionality least-square problems are solved using well-selected subsets from the input data. The results of this initial approach are fed into the LMedS schema, which is applied to recover the final estimation of the Fundamental matrix. The complexity is substantially reduced by applying a selection process based on an effective statistical analysis of the inherent correlation of the input data. This analysis is used to define a suitable clustering of the data and to drive the subset selection aiming at the reduction of the search space in the LMedS schema. It is shown that avoiding redundancies better estimates can be obtained while keeping the computational cost low. Selected results of computer experiments were conducted to assess the performance of the proposed technique.

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Computer experiments to find the minimum lower unity of a monotone Boolean function

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(90)90063-x ◽

1990 ◽

Vol 30 (4) ◽

pp. 196-203

Author(s):

V.G. Ustyuzhaninov

Keyword(s):

Boolean Function ◽

Computer Experiments ◽

Monotone Boolean Function

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A New Pairwise NPN Boolean Matching Algorithm Based on Structural Difference Signature

Symmetry ◽

10.3390/sym11010027 ◽

2018 ◽

Vol 11 (1) ◽

pp. 27

Author(s):

Juling Zhang ◽

Guowu Yang ◽

William Hung ◽

Jinzhao Wu ◽

Yixin Zhu

Keyword(s):

North Carolina ◽

Boolean Function ◽

Structural Difference ◽

Search Space ◽

Experimental Results ◽

Matching Algorithm ◽

Matching Process ◽

Boolean Matching ◽

Run Time

In this paper, we address an NPN Boolean matching algorithm. The proposed structural difference signature (SDS) of a Boolean function significantly reduces the search space in the Boolean matching process. The paper analyses the size of the search space from three perspectives: the total number of possible transformations, the number of candidate transformations and the number of decompositions. We test the search space and run time on a large number of randomly generated circuits and Microelectronics Center of North Carolina (MCNC) benchmark circuits with 7–22 inputs. The experimental results show that the search space of Boolean matching is greatly reduced and the matching speed is obviously accelerated.

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