Difference between revisions of "Tribes"
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| − | The tribe function with <math>t</math> tribes of size | + | == Definition == |
| + | The tribe function with <math>t</math> tribes of size <math>n</math> is the boolean function <math>\mathrm{Tribes}_{t,n} : \{-1 ,+1\}^{tn} \rightarrow \{-1,+1\}</math> defined by the DNF formula | ||
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| + | :<math>\mathrm{Tribes}_{t,n}(x) = \bigvee_{i=1}^{t} \bigwedge_{j=1}^{n} x_{i,j}</math>, | ||
| + | |||
| + | where we identify <math>-1</math> with logical True and <math>+1</math> with logical False. | ||
Revision as of 11:00, 2 September 2018
Definition
The tribe function with [math]t[/math] tribes of size [math]n[/math] is the boolean function [math]\mathrm{Tribes}_{t,n} : \{-1 ,+1\}^{tn} \rightarrow \{-1,+1\}[/math] defined by the DNF formula
- [math]\mathrm{Tribes}_{t,n}(x) = \bigvee_{i=1}^{t} \bigwedge_{j=1}^{n} x_{i,j}[/math],
where we identify [math]-1[/math] with logical True and [math]+1[/math] with logical False.
