Kettle, Neil and King, Andy (2006) Proof of New Implicational Relationships between Generalized Symmetries (appendix for journal paper). University of Kent, School of Computing, University of Kent, Canterbury, Kent, CT2 7NF, 11 pp. (Full text available)
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Abstract
This note provides proof of some new implicational relationships between generalized symmetries. These relationships are formulated in terms of twelve symmetry types. Six of these symmetries are denoted T<sub>n</sub><sup>x<sub>i</sub>,x<sub>j</sub></sup> where the index n∈[1,6] indicates that a specific cofactor equivalence property holds between the variables x<sub>i</sub> and x<sub>j</sub>. The other six symmetries are denoted neg T<sub>n</sub><sup>x<sub>i</sub>,x<sub>j</sub></sup>, and indicate that one cofactor is equivalent to the negation of the other. The relationships that are specified take the form, if T<sub>p</sub><sup>x<sub>i</sub>,x<sub>j</sub></sup> and T<sub>q</sub><sup>x<sub>j</sub>,x<sub>k</sub></sup> hold then T<sub>r</sub><sup>x<sub>i</sub>,x<sub>j</sub></sup> holds where T<sub>p</sub>,T<sub>q</sub> and T<sub>r</sub> denote one of these twelve symmetry types.
Item Type:  Research report (external) 

Uncontrolled keywords:  Boolean functions 
Subjects:  Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming, 
Divisions:  Faculties > Science Technology and Medical Studies > School of Computing > Theoretical Computing Group 
Depositing User:  Andy King 
Date Deposited:  24 Nov 2008 18:04 
Last Modified:  28 May 2014 08:48 
Resource URI:  https://kar.kent.ac.uk/id/eprint/14501 (The current URI for this page, for reference purposes) 
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