Hello there,
I came up with a way to assign a unique number (whole number) between 0 and 2^(2^n)-1 to each Boolean function of n Boolean variables.
I have a couple questions:
1) Do you think this may have any interesting applications?
2) Have you seen before a similar type of functional? (A function from the set of Boolean functions to the set of whole numbers).
This would be an expression for the general formula:
N(f) = Sum(over all Boolean/Binary vectors x1,..,xm; f(x1,..xm) times 2^Sum(for k=1,..,m; xk times 2^(k-1) ) )
The number is calculated from the Boolean function by interpreting "True" as "1" and "False" as "0," and then evaluating a polynomial of powers of two, with coefficients given by the function, and exponents also being themselves polynomials of powers of two, with coefficients given by the variables, and exponents given by the sub-indexes of the variables (minus 1).
I have posted additional details in this page:
http://www.sdmath.com/math/boolean.html
Please take a look because I appreciate very much any feedback, questions, comments, and/or suggestions about this linear ordering of Boolean functions.
Thanks.
I came up with a way to assign a unique number (whole number) between 0 and 2^(2^n)-1 to each Boolean function of n Boolean variables.
I have a couple questions:
1) Do you think this may have any interesting applications?
2) Have you seen before a similar type of functional? (A function from the set of Boolean functions to the set of whole numbers).
This would be an expression for the general formula:
N(f) = Sum(over all Boolean/Binary vectors x1,..,xm; f(x1,..xm) times 2^Sum(for k=1,..,m; xk times 2^(k-1) ) )
The number is calculated from the Boolean function by interpreting "True" as "1" and "False" as "0," and then evaluating a polynomial of powers of two, with coefficients given by the function, and exponents also being themselves polynomials of powers of two, with coefficients given by the variables, and exponents given by the sub-indexes of the variables (minus 1).
I have posted additional details in this page:
http://www.sdmath.com/math/boolean.html
Please take a look because I appreciate very much any feedback, questions, comments, and/or suggestions about this linear ordering of Boolean functions.
Thanks.