  Symbolic Regression (SR) allows for the discovery of scientific equations
from data. To limit the large search space of possible equations, prior
knowledge has been expressed in terms of formal grammars that characterize
subsets of arbitrary strings. However, there is a mismatch between context-free
grammars required to express the set of syntactically correct equations,
missing closure properties of the former, and a tree structure of the latter.
Our contributions are to (i) compactly express experts' prior beliefs about
which equations are more likely to be expected by probabilistic Regular Tree
Expressions (pRTE), and (ii) adapt Bayesian inference to make such priors
efficiently available for symbolic regression encoded as finite state machines.
Our scientific case studies show its effectiveness in soil science to find
sorption isotherms and for modeling hyper-elastic materials.
