| In this thesis, we use syntactic congruences of languages, syntactic monoids of languages and infix languages of languages to study the characterizations, the de-compositions and the classifications of r-disjunctive languages. Firstly, we use the syntactic congruences to give a classification of r-disjunctive languages as follow: Dr=∪4i=1Di; and then we use some construction techniques, including the use of solid codes, to give a kind of decompositions of r-disjunctive languages, that is, there exist languages in Di which can be divided into two languages, both of which are in Di+1, i=1,2,3. Secondly, we characterize the disjunctive degrees in the sense of two levels about the r-disjunctive languages. On the one hand, we discuss the disjunc-tive degrees of r-disjunctive languages from D1to D4, on the other hand, we intro-duce the concepts of infix-i-disjunctive languages, use infixes to classify the Di and get the completely infix-i-disjunctive languages, properly partially infix-i-disjunctive languages, trivially infix-i-disjunctive languages, i=1,2,3,4, this is the i-disjunctive degrees of r-disjunctive languages, especially, if i=1, then this is the disjunctive degrees of r-disjunctive languages. Moreover, for the above discussions, we have es-tablished a new result for r-regular languages, that is, the concatenation of r-regular languages and finite languages is also r-regular languages. This result is meaningful, because it is well known that the r-regular languages are not closed under the oper-ation of concatenation. Thirdly, we give an improved algorithm about a disjunctive decomposition of dense languages. Finally, we discuss some properties of completely infix-disjunctive languages. |
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