  We discuss general properties of classical string field theories with
symmetric vertices in the context of deformation theory. For a given conformal
background there are many string field theories corresponding to different
decomposition of moduli space of Riemann surfaces. It is shown that any
classical open string field theories on a fixed conformal background are
$A_\infty$-quasi-isomorphic to each other. This indicates that they have
isomorphic moduli space of classical solutions. The minimal model theorem in
$A_\infty$-algebras plays a key role in these results. Its natural and
geometric realization on formal supermanifolds is also given. The same results
hold for classical closed string field theories, whose algebraic structure is
governed by $L_\infty$-algebras.
