While modelling a discrete-time system, it is natural to assign a
sequence of numbers in which the i-th number
is equal to the value of the parameter at the i-th moment in time to
every parameter of the system.
There are usually several parameters with some relations among them.
For every i-th moment in time, these relations can be written as
equations in the values of the parameters at this moment and some
neighboring moments. It is assumed that these equations are the same
for all moments in time up to shifting the indices.
A natural question to ask is whether such an infinite system of
equations corresponding to the model has a solution.
In this talk, we will describe cases in which this problem can be
solved algorithmically using effective upper bounds.
This is joint work with Alexander Levin and Alexey Ovchinnikov.