Finite Language Forbidding-Enforcing Systems

The forbidding and enforcing paradigm was introduced by Ehrenfeucht and Rozenberg as a way to define families of languages based on two sets of boundary conditions. Later, a variant of this paradigm was considered where an fe-system defines a single language. We investigate this variant further by studying fe-systems in which both the forbidding and enforcing sets are finite and show that they define regular languages. We prove that the class of languages defined by finite fe-systems is strictly between the strictly locally testable languages and the class of locally testable languages.