Branching Programs, Grammar Systems and the NC1 Class

Cooperating distributed grammar systems (CDGSs) are sets of Chomsky grammars that work sequentially on a common sentential form according to a specified protocol of cooperation. Branching programs (BPs) are fundamental models of non-uniform computation that simultaneously capture time and space in sequential computation. In this paper we deal with simulations of CDGSs by bounded width branching programs (BWBPs). We present several lower and upper bounds for time, space and cooperation (communication) complexity measures for CDGSs that emerge from these simulations. It is widely known that the class of languages recognizable by BWBPs equals the NC¹ class, i.e., the class of languages recognizable by fan-in two, logarithmic-depth and polynomial-size uniform Boolean circuits. With respect to this result and the simulations presented in this paper, the class of the Szilard languages associated to derivations in CDGSs are related to the NC¹ class.