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Proof of New Implicational Relationships between Generalized Symmetries
Neil Kettle and Andy King
Technical Report 13-05, University of Kent, Computing Laboratory, University of Kent, Canterbury, Kent, CT2 7NF, February 2006.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 (unknown variable T_){n}^{x_i,x_j}$ where the index (unknown variable n)\in[1,6]$ indicates that a specific co-factor equivalence property holds between the variables (unknown variable x_i)$ and (unknown variable x_j)$. The other six symmetries are denoted $\neg T_{n}^{x_i,x_j}$, and indicate that one co-factor is equivalent to the negation of the other. The relationships that are specified take the form, if (unknown variable T_){p}^{x_i,x_j}$ and (unknown variable T_){q}^{x_j,x_k}$ hold then (unknown variable T_){r}^{x_i,x_j}$ holds where (unknown variable T_){p},T_{q}$ and (unknown variable T_){r}$ denote one of these twelve symmetry types.
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@techreport{2349,
author = {Neil Kettle and Andy King},
title = {Proof of {N}ew {I}mplicational {R}elationships between {G}eneralized {S}ymmetries},
month = {February},
year = {2006},
pages = {11},
keywords = {Boolean functions},
note = {},
doi = {},
url = {http://www.cs.kent.ac.uk/pubs/2006/2349},
publication_type = {techreport},
submission_id = {28296_1138983113},
number = {13-05},
address = {University of Kent, Canterbury, Kent, CT2 7NF},
institution = {University of Kent, Computing Laboratory},
}