Functions of k-valued logic

[Adolf2008]

Represent the function f (x, y) = min (x, y) as a polynomial modulo 3 (k = 3). How can i do that? Is there a special algorithm?

 

[Dr.Peterson]

It may be necessary for you to show us what kind of k-valued logic you are learning. In particular, were you given any examples using polynomials mod k?

 

[Adolf2008]

It may be necessary for you to show us what kind of k-valued logic you are learning. In particular, were you given any examples using polynomials mod k?

All i have is theorem and solution for one variable function

 

[Adolf2008]

1) min(x,y) = j₁(x)j₁(y)+j₁(x)j₂(y)+j₂(x)j₁(y)+2j₂(x)j₂(y), j_i(x) = j₀(x-i), j₀(x) = 1-x^k-1
2) min(x,y) = (1-(x-1)²)(1-(y-1)²)+(1-(x-1)²)(1-(y-2)²)+(1-(x-2)²)(1-(y-1)²)+2(1-(x-2)²)(1-(y-2)²) = 5x²y²-16x²y-16xy²+52xy+9x²+9y²-30x-30y+18
Solution: 5x²y²-16x²y-16xy²+52xy+9x²+9y²-30x-30y+18 (mod 3)

 

[Dr.Peterson]

1) min(x,y) = j₁(x)j₁(y)+j₁(x)j₂(y)+j₂(x)j₁(y)+2j₂(x)j₂(y), j_i(x) = j₀(x-i), j₀(x) = 1-x^k-1
2) min(x,y) = (1-(x-1)²)(1-(y-1)²)+(1-(x-1)²)(1-(y-2)²)+(1-(x-2)²)(1-(y-1)²)+2(1-(x-2)²)(1-(y-2)²) = 5x²y²-16x²y-16xy²+52xy+9x²+9y²-30x-30y+18
Solution: 5x²y²-16x²y-16xy²+52xy+9x²+9y²-30x-30y+18 (mod 3)

Is this a solution you were given, or one you worked out? I don't follow the details of your work.

Of course you could simplify your answer (mod 3) to 2x²y²-x²y-xy²+xy, right? That makes it a little easier to check.

 

[Adolf2008]

Is this a solution you were given, or one you worked out? I don't follow the details of your work.

Of course you could simplify your answer (mod 3) to 2x²y²-x²y-xy²+xy, right? That makes it a little easier to check.

I found it out from the book. How could you simplify this function? I will be grateful for a link to the literature about it