Monotone separation of logspace from NC/sup 1/

Abstract

It is shown that the monotone analog of logspace computation is more powerful than monotone log-depth circuits: monotone circuits for a certain function in monotone logspace require depth Omega (lg/sup 2/n). It is proved that mNC/sup 1/ not=mL. This result shows that the process of pointer jumping, i.e. following a chain of pointers to the end, cannot be simulated by a monotone NC/sup 1/ circuit. The proof is based upon the communication game method of A. Karchmer and A. Wigderson (1990).<>