One-way two-counter machines represent a universal model of computation. Here we consider the polynomial-time classes of multicounter machines with a constant number of reversals and separate the computational power of nondeterminism, randomization and determinism. For instance, we show that polynomial-time one-way multicounter machines, with error probability tending to zero with growing input length, can recognize languages that cannot be accepted by polynomial-time nondeterministic two-way multicounter machines with a bounded number of reversals. A similar result holds for the comparison of determinism and one-sided-error randomization, and of determinism and Las Vegas randomization. © 2004 Elsevier B.V. All rights reserved.
Hromkovi, J., & Schnitger, G. (2005). On the power of randomized multicounter machines. Theoretical Computer Science, 330(1), 135–144. https://doi.org/10.1016/j.tcs.2004.09.015