What are barriers to Genetic Programming with cyclic graphs Genetic programming uses either trees (in case of classical GP) or acyclic graphs (CGP and in a certain sense LGP), to represent evolved programs (phenotypes).

Is there any reason, why cyclic graphs aren't used?
Perhaps one reason is that constraints (perhaps somewhat arbitrary ones) would have to be imposed on what it means to interpret a program represented in this fashion.

However, recent work with CGP has actually explored the addition of cycles:
Recurrent CGP