A Uniform Framework for Language Inclusion Problems

We present a uniform approach for solving language inclusion problems. Our approach relies on a least fixpoint characterization and a quasiorder to compare words of the "smaller" language, reducing the inclusion check to a finite number of membership queries in the "larger" language. We present our approach in detail on the case of inclusion of a context-free language given by a grammar into a regular language. We then explore other inclusion problems and discuss how to apply our approach.