An Explicit Expression for MZVs in Terms of Symmetric MZVs

We provide a simpler proof of the fact, originally proved by Seidai Yasuda, that symmetric multiple zeta values generate the entire space of multiple zeta values. Furthermore, based on this argument, we present an algorithm for expressing multiple zeta values in terms of symmetric multiple zeta values and products of multiple zeta values. Moreover, we give some results on symmetric and finite multiple zeta values of depth three.