Computational Parallels between the Regular and Context-Free Languages

Several sufficient conditions are presented for a regular set or context-free language problem to be as hard as testing for emptiness or testing for equivalence to the language $\{ 0,1\} ^ * $. These sufficient conditions provide a unified method for proving undecidability or complexity results and apply to a large number of language problems studied in the literature. Many new nonpolynomial lower complexity bounds and undecidability results follow easily. The techniques used to prove these sufficient conditions involve reducibilities utilizing simple and efficient encodings by homomorphisms.