Two polynomials f and g are said to be algebraically dependent over a field K if there exists a non-zero bivariate polynomial A with coefficients in K such that A(f,g)=0. If no such polynomial exists, we say that f and g are independent. This is a natural generalization of linear independence to higher degrees. We consider the problem of finding an algorithm to test whether the given set of polynomials are algebraically independent. When the field has characteristic zero, this problem has a randomised polynomial time algorithm using the Jacobian Matrix of the given polynomials. However the criterion fails when the polynomials are taken over the fields of positive characteristic. One can expect that the positive characteristic case also has an efficient algorithm for testing algebraic independence, however, the existing best known upper bound is very far from desired. The talk will cover a result which is an attempt to bridge this gap. We present a new algorithm which is based on a refined generalisation of Jacobian criterion in case of fields of positive characteristic. It also yields a structural result about the algebraically dependent polynomials - approximate functional dependence.