  We study systems of String Equations where block variables need to be
assigned strings so that their concatenation gives a specified target string.
We investigate this problem under a multivariate complexity framework,
searching for tractable special cases such as systems of equations with few
block variables or few equations. Our main results include a polynomial-time
algorithm for size-2 equations, and hardness for size-3 equations, as well as
hardness for systems of two equations, even with tight constraints on the block
variables. We also study a variant where few deletions are allowed in the
target string, and give XP algorithms in this setting when the number of block
variables is constant.
