“…Recall that two pieces (M, m), (M , m ) are ≈-equivalent if their incompatible sets are equal, that is, if I(M, m) = I(M , m ). By Definition 4.4, the signature τ is finite if and only if ≈ has finitely many equivalence classes on the pieces of the trees contained in F. In this case, we call F a regular class of σ-trees; the term is motivated by a connection to regular languages, highlighted in [9]. This definition of regularity coincides with the one from [16].…”