We present a class of boolean functions which have regional mappings, a generalization of the transitivity property de- fined in [12]. We prove that all transitive problems have regional mappings, as do a variety of interesting computa- tional problems such as merging two sorted lists of arbitrary length, generalized integer multiplication and matrix-vector products. We present a general area-time lower bound for VLSI implementations of problems with regional mappings and confirm that the lower bound matches the previously known bound for transitive problems. For generalized inte- ger multiplication, we present a custom VLSI implementa- tion which provides a matching upper bound. The results improve AT2 bounds on a number of open problems. In related work, we consider the problem of finding oc- currences of a P-bit pattern in an N-bit text string. We show that every chip capable of solving this string matching problem requires AT2 = (PN). A custom VLSI design, using an idea similar to that used for generalized integer multiplication, provides a matching upper bound when N is polynomial in P.