Enhancements to Crisp Possibilistic

 Reconstructability Analysis

 Anas N. Al-Rabadi⁽¹⁾ and Martin Zwick⁽²⁾

(1) ECE Department    (2) Systems Science Ph.D. Program 

Portland State University

[alrabadi@ece.pdx.edu] ⁽¹⁾, [zwick@sysc.pdx.edu] ⁽²⁾

Keywords: Reconstructability Analysis, Ashenhurst-Curtis Decomposition, Boolean Functions, NPN-Classification, Log-Functionality Complexity Measure.

 Abstract

Modified Reconstructibility Analysis (MRA), a novel decomposition within the framework of set-theoretic (crisp possibilistic) Reconstructibility Analysis, is presented. It is shown that in some cases while 3-variable NPN-classified Boolean functions are not decomposable using Conventional Reconstructibility Analysis (CRA), they are decomposable using Modified Reconstructibility Analysis (MRA). Also, it is shown that whenever a decomposition of 3-variable NPN-classified Boolean functions exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. A comparison of the corresponding complexities for Ashenhurst-Curtis decompositions, and Modified Reconstructibility Analysis (MRA) is also presented. While both AC and MRA decompose some but not all NPN-classes, MRA decomposes more classes, and consequently more Boolean functions. MRA for many-valued functions is also presented, and algorithms using two different methods (intersection and union) are given. A many-valued case is presented where CRA fails to decompose but MRA decomposes.

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