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language ESSENCE 1.3.0
 
$ Problem Equidistant Frequency Permutation Arrays
$
$ Problem details available at http://www.csplib.org/Problems/prob055/
$
$ Essence model by Andrew Martin
$
$ Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/
 
given v : int(1..)
given d : int(1..)
given q : int(1..)
given lam : int(1..)
 
letting dSequnce be domain int(1..q*lam)
letting dElement be domain int(1..q)
 
find E : set (size v) of matrix indexed by [dSequnce] of dElement
 
$ each element in (1..q) must occur lambda times per sequence
such that
    forAll m in E .
        forAll element : dElement .
            (sum index : dSequnce . toInt(m[index] = element)) = lam
 
$ each non-identical pair must be hamming distance d apart
such that
    forAll seqA, seqB in E .
        seqA = seqB
        \/
        (sum index : dSequnce . toInt(seqA[index] != seqB[index])) = d