**A. Hajnal, W. Maass, P. Pudlak, M. Szegedy, and G. Turan**

We examine a powerful model of parallel computation: polynomial size threshold
circuits of bounded depth (the gates compute threshold functions with
polynomial weights). Lower bounds are given to separate polynomial size
threshold circuits of depth 2 from polynomial size threshold circuits of
depth 3 and from probabilistic polynomial size circuits of depth 2. With
regard to the unreliability of bounded depth circuits, it is shown that the
class of functions computed reliably with bounded depth circuits of
unreliable
gates is narrow. On the other hand, functions
computable by bounded depth, polynomial-size threshold circuits can also be
computed by such circuits of unreliable threshold gates. Furthermore we
examine to what extent imprecise threshold gates (which behave unpredictably
near the threshold value) can compute nontrivial functions in bounded depth
and a bound is given for the permissible amount of imprecision. We also
discuss threshold quantifiers and prove an undefinability result for graph
connectivity.