We view a genotype as a vector of sites, each site having a value from the domain {0, 1, 2}; and a haplotype as a vector of sites, each site having a value from the domain {0, 1}. According to Brown, a genotype is ambiguous if its value is 1; and resolved otherwise. Two haplotypes h1 and h2 form (or explain) a genotype g if for every site j the following hold:

 

g[j] = h1[j]+ h2[j]

 

For instance, the genotype 20110 can be explained by the haplotypes 10010 and 10100:

 

10010

10100

-------

20110

 

Consider a set H of k haplotypes. For the problem above, H is a solution to HIPP-DEC if the following constraints are satisfied:

 

C1'       For every genotype g in G, there exist two haplotypes h1 and h2 in H such that, for every site j, g[j] = h1[j]+ h2[j].