Computing Permanents over Fields of Characteristic 3: Where and Why It Becomes Difficult (extended abstract)
نویسنده
چکیده
36 instance of the satissability problem we associate a set of such matrices. The instance is called 1?semi?unitary if there is at least one 1?semi?unitary matrix in this set. Now 1 ? SEMI ? UNISAT is the satissability problem restricted to 1 ? semi ? unitary instances, KMb]. Given such parameters, 1 ? SEMI ? UNISAT can be solved in polynomial time. Problem 7.3 What is the complexity that we can nd such parameters. Are there any eecient heuristics for nding such parameters ? The corresponding satissability problem UNISAT, for unitary matrices, turns out to be trivial and therefore solvable in polynomial time. The rst author is currently writing his Ph.D. thesis Kog] on the complexity of Schur functions in rings and elds of various characteristics. Schur functions are generalizations of the permanent and determinant and include the Hamiltonian and other combinatorial counting polynomials, cf. BCS97, GJ83]. His results for characteristic 2 are presented in Kog, KMa]. References Bar96] A.I. Barvinok. Two algorithmic results for the traveling salesman problem. where the indices k a;b do not belong to the path. More precisely, let =
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