  We establish generalizations of the well-known surjunctivity theorem of
Gromov and Weiss as well as the dual-surjunctivity theorem of Capobianco, Kari
and Taati for cellular automata (CA) to local perturbations of CA over sofic
group universes. We also extend the results to a class of non-uniform cellular
automata (NUCA) consisting of global perturbations with uniformly bounded
singularity of CA. As an application, we obtain the surjunctivity of algebraic
NUCA with uniformly bounded singularity over sofic groups. Moreover, we prove
the stable finiteness of twisted group rings over sofic groups to generalize
known results on Kaplansky's stable finiteness conjecture for group rings.
