  In this paper we present a method of characteristic sets for inversive
difference polynomials and apply it to the analysis of systems of quasi-linear
algebraic difference equations. We describe characteristic sets and compute
difference dimension polynomials associated with some such systems. Then we
apply our results to the comparative analysis of difference schemes for some
PDEs from the point of view of their Einstein's strength. In particular, we
determine the Einstein's strength of standard finite-difference schemes for the
Murray, Burgers and some other reaction-diffusion equations.
