F. Afrati et Ch. Papadimitriou, THE PARALLEL COMPLEXITY OF SIMPLE LOGIC PROGRAMS, Journal of the Association for Computing Machinery, 40(4), 1993, pp. 891-916
We consider logic programs with a single recursive rule, whose right-h
and side consists of binary relations forming a chain. We give a compl
ete characterization of all programs of this form that are computable
in NC (assuming that P not-equal NC). Our proof uses ideas from automa
ta and language theory, and the combinatories of strings.