Pseudo-Boolean Constraint Formulation of Symmetry Boolean Encoding for Multi-Valued Function

• Main Authors: Meng-Yen Li, 李孟彥
• Other Authors: Jie-Hong Jiang
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/77262853728488075866

碩士 === 國立臺灣大學 === 電子工程學研究所 === 99 === In high level designs, variables are often represented in the form of symbolic multi-values. The realization of multi-valued logic in bit level is called encoding and selecting the appropriate encoding would be a challenging and difficult problem. Prior literatures showed that it is hard to foresee the effect of chosen encoding after powerful logic optimization. To the best of our knowledge, choosing encoding biased for some special functional property is never studied before except minimizing area. Since symmetry is the most studied and applied functional property, we would like weave this property into encoding when implement multi-valued function. Symmetric Boolean functions have many useful applications in various aspects. In cryptography, they have special cryptographic parameters. It is easier to optimize symmetric functions in physical design domain. They also applied in fault testability in BDD based synthesis. In this work, we define and study the Symmetry Encoding Problem (SEP) as a problem to maximize the symmetries of encoded function when realizing multi-valued function. We also propose a systematic method to model the SEP into Pseudo-Boolean Constraint (PBC). Using existing constraint optimizer like IBM ILOG CPLEX Optimizer(TM) we can solve and generate the solution of SEP. Besides totally symmetric function, the method can also target for partially symmetric function. Experiments show that by PBC solving, the symmetric encoding generated will encode multi-valued function with more symmetries in a large portion of test cases while compared with naive encoding (encode multi-value in binary representation directly). This method has promising result for small size circuits, which has less than 6 of inputs after encoding (up to 64 multi-values). However it has critical weaknesses, i.e. scalability. This method is also not available for multiple outputs. We would like overcome these weaknesses in future work.