On efficient simulations of multicounter machines

Abstract

An oblivious 1-tape Turing machine can simulate a multicounter machine on-line in linear time and logarithmic space. This leads to a linear cost combinational logic network implementing the first n steps of a multicounter machine and also to a linear time/logarithmic space on-line simulation by an oblivious logarithmic cost RAM. An oblivious log* n -head tape unit can simulate the first n steps of a multicounter machine in real-time, which leads to a linear cost combinational logic network with a constant data rate.