THE PARALLEL COMPLEXITY OF PROPAGATION IN BOOLEAN CIRCUITS

We consider the problem of deciding whether the output of a boolean circuit is determined by a partial assignment to its inputs. This problem is easily shown to be hard, i.e., co-NP-complete. However, many of the consequences of a partial input assignment may be determined in linear time, by iterating the following step: if we know the values of some inputs to a gate, we can deduce the values of some outputs of that gate. This process of iteratively deducing some of the consequences of a partial assignment is called propagation. This paper explores the parallel complexity of propagation, i.e., the complexity of determining whether the output of a given boolean circuit is determined by propagating a given partial input assignment. We give a complete classification of the problem into those cases that are p-complete and those that are unlikely to be p-complete. (C) 1995 Academic Press. Inc.