  Symbolic regression (SR) is the task of discovering a symbolic expression
that fits a given data set from the space of mathematical expressions. Despite
the abundance of research surrounding the SR problem, there's a scarcity of
works that confirm its NP-hard nature. Therefore, this paper introduces the
concept of a symbol graph as a comprehensive representation of the entire
mathematical expression space, effectively illustrating the NP-hard
characteristics of the SR problem. Leveraging the symbol graph, we establish a
connection between the SR problem and the task of identifying an optimally
fitted degree-constrained Steiner Arborescence (DCSAP). The complexity of
DCSAP, which is proven to be NP-hard, directly implies the NP-hard nature of
the SR problem.
