On the regularity of matrices in min algebra

Abstract We consider the concept of regularity for square matrices with entries from a linearly ordered commutative group ( G ,+,⩾), the algebraic compositions being given by x ⊕ y = min ( x , y ), x ⊗ y = x + y . For the case where G is cyclic we derive a necessary and sufficient condition for the regularity of a matrix, which can be checked in O ( n 3 ) operations using standard algorithms.