In this paper, algorithms for the computation of all matrices of the generalized polynomial Bezout identity are proposed. The algorithms are based on the computation of minimal polynomial basis for the right null spaces of certain polynomial matrices. For this reason, an algorithm for the computation of minimal polynomial bases is also proposed. Since this algorithm relies solely on singular va...

We show that all minimal dominating sets of a chordal bipartite graph can be generated in incremental polynomial, hence output polynomial, time. Enumeration of minimal dominating sets in graphs is equivalent to enumeration of minimal transversals in hypergraphs. Whether the minimal transversals of a hypergraph can be enumerated in output polynomial time is a well-studied and challenging questio...

This paper formulates the problem of determining the degrees of all polynomial entries in a minimal polynomial basis of a polynomial matrix by using only the degree structure of the given matrix. Using a block Toeplitz matrix structure corresponding to the given polynomial matrix, it is shown that the degrees of the elements in its minimal polynomial basis, in the generic case, depend only on t...

—The problem of determination of a minimal polynomial basis of a rational vector space is the starting point of many control analysis, synthesis and design techniques. In this paper, we propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F (s). The proposed method exploits the structure of the left null space of generalized W...