The Inclusion Problem for Some Subclasses of Context-Free Languages

− By a reduction to Post’s Correspondence Problem we provide a direct proof of the known fact that the inclusion problem for unambiguous context-free grammars is undecidable. The argument or some straightforward modification also applies to some other subclasses of context-free languages such as linear languages, sequential languages, and DSClanguages (i.e., languages generated by context-free grammars with disjunct syntactic categories). We also consider instances of the problem “Is L ( D1) ⊆ L ( D2)?” where D1 and D2 are taken from possibly different descriptor families of subclasses of context-free languages.