Algorithmic Properties of Structures for the Language with Two Unary Functional Symbols

When studying algorithmic properties of structures with interesting algebraic and model-theoretic properties, one often uses known structural properties of the structures. However, it is often the case that results on particular kinds of structures can be transferred to structures from many other interesting classes. One of the ways of such generalization involves coding of the original structure into a structure from the given class in a way that is effective enough to preserve interesting algorithmic properties. There are several constructions that allow us to reduce algorithmic questions for arbitrary structures to graphs. They also show that if we have a result for a graph, we also have it for a structure for any language containing at least one $n$-ary relational symbol, where $n\geq 2$. We prove that it is possible to generalize this approach and get the same results for structures for a language with two unary functional symbols. Thus, we get the results for structures for so–called rich languages.