The problem with performance of genetic programming (GP) comes in part from what descrip-tion tool we use and what convenience it may offer. As random search technologies, a major challenge GP must face is to get ideal approaches for depicting the search space and evolution rules. To this end, model ap-proaches aiming to delineate relationships among given components or constructors is initiated under finite state transition systems, and a deep investigation into efficient implementation of genetic operators is carried out. To make it more convincing, we also conduct experiments with classical regression problems, obtaining positive result from comparisons between the present approach and an important GP variant like grammatical evolution.