On f-Disjunctive Languages, f-Disjunctive Domains and Solid Codes(Dedicated to the late Professor Xu Yonghua (1932-2019))

Every language is either the disjoint union or the intersection of two disjunctive languages.The family of f-disjunctive languages is a natural generalization of the family of disjunctive languages.Disjunctive domains(f-disjunctive domains)are defined as the languages which can be checked whether a given language is disjunctive(f-disjunctive)or not.The f-disjunctive domains were first studied by Guo et al.around 1986-1989.We continue their study on f-disjunctive domains.Some new results for f-disjunctive domains,containing a relation between disjunctive domains and f-disjunctive domains,are introduced.In this respect,we also make an appropriate opening for the completely dense languages and solid codes.

Solid codes and the uniform density of fd-domains

By means of further investigation of solid codes,the problem“Is every fd-domain uni- formly dense”proposed by Yuqi Guo,C.M.Reis and G.Thierrin in 1988 is solved in this paper.