Solid Codes And R-disjunctive Languages

In this thesis,we mainly use solid codes and syntactic congruences to study languages.Firstly,a binary operation*is defined in l(S),where S is a solid code over the alphabet A,and(l(S),*)is proved to be a monoid.In monoid(l(S),*),the idempotents and regular elements are characterized.Secondly,A new simple proof is given to prove that:the congruence as determined by the solid code S is a principal congruence.Two another congruences As and ps are defined by using the solid code S,and they are also proved to be principal congruences.Third-ly,the concatenation of thin languages and r-disjunctive languages are discussed.It is proved that the concatenation of a thin language and L is a disjunctive(f-disjunctive,t-disjunctive)language implies that L is a disjunctive(f-disjunctive,t-disjunctive)language.Some examples are given to show that the concatenation of a thin language and L is a i-disjunctive(r-disjunctive)language,but L is not a i-disjunctive(r-disjunctive)language.Finally,some new examples of the decompo-sitions of the r-disjunctive languages are given,and a character to the semigroup with dense-disjunctive property is given.