A Simple Algorithm for Hamiltonicity

We develop a new algebraic technique that solves the following problem: Given a black box that contains an arithmetic circuit f over a field of characteristic 2 of degree d. Decide whether f , expressed as an equivalent multivariate polynomial, contains a multilinear monomial of degree d. This problem was solved by Williams [4] and Björklund et. al. [5] for a white box (the circuit is given as an input) that contains arithmetic circuit. We show a simple black box algorithm that solves the problem with the same time complexity. This gives a simple randomized algorithm for the simple k-path problem for directed graphs of the same time complexity1 O∗(2k) as in [4] and with reusing the same ideas from [5] with the above gives another algorithm (probably not simpler) for undirected graphs of the same time complexity O∗(1.657k) as in [1, 5].