Mathematical foundations of linearization algorithms: reflexive-transitive closures of binary relations

Анотація

The paper is devoted to the mathematical foundations of the linearization algorithms – one of the methods of names conflict resolution that occurs in object-oriented programming languages which support multiple inheritance. The main object of study is the reflexive-transitive closure of a binary relation. The basic properties of this closure are found: the criterion to be partial order, closure is the closure operator with respect to the set-theoretic inclusion, three denotation representations of closure in terms of its properties and as the least solution of some characteristic equation are established (the structure of the set of all solutions of this equation is found).