Special Section: Theory of Computation

simply check whether all coefficients 1 2 , ,..., n i i i c F  are zero. The problem becomes non-trivial when the polynomial is given in an implicit form, e.g. as determinant of a matrix with polynomial entries. One can compute the determinant polynomial to express it in the above form. However, the size of the polynomial can grow exponentially in this process and so this algorithm is exponential overtime. Finding an efficient algorithm for the problem has over the years become one of the most important challenges in complexity theory with fundamental implications. A general representation of polynomials is via arithmetic circuits: these define a sequence of addition and multiplication operations starting from variables and ending in the desired polynomial. For example