  In the article differential-difference (semi-discrete) lattices of hyperbolic
type are investigated from the integrability viewpoint. More precisely we
concentrate on a method for constructing generalized symmetries. This kind
integrable lattices admit two hierarchies of generalized symmetries
corresponding to the discrete and continuous independent variables $n$ and $x$.
Symmetries corresponding to the direction of $n$ are constructed in a more or
less standard way while when constructing symmetries of the other form we meet
a problem of solving a functional equation. We have shown that to handle with
this equation one can effectively use the concept of characteristic
Lie-Rinehart algebras of semi-discrete models. Based on this observation, we
have proposed a classification method for integrable semi-discrete lattices.
One of the interesting results of this work is a new example of an integrable
equation, which is a semi-discrete analogue of the Tzizeica equation. Such
examples were not previously known.
