Abstract It follows from Michael’s selection theory that a closed convex nonempty-valued mapping the Sorgenfrey line to euclidean space is inner semicontinuous if and only can be represented as image closure of right-continuous selections mapping. This article gives necessary sufficient conditions for representation hold càdlàg selections, i.e., are have left limits. The characterization motiva...

This paper presents a nice Turing characterization of important classes of multivalued functions (used to model search problems) which elucidates properties of such classes as well as relationships among them. The results are based on a Turing transducer, called writenondeterministic (WND) transducer, which extends deterministic Turing machines with a simple non-deterministic construct which le...

This paper surveys basic results on complexity classes of partial multivalued functions. We stress basic inclusion relations, interesting hierarchies, and results that demonstrate that hierarchies are extant.

The class TFNP, defined by Megiddo and Papadimitriou, consists of multivalued functions with values that are polynomially verifiable and guaranteed to exist. Do we have evidence that such functions are hard, for example, if TFNP is computable in polynomial-time does this imply the polynomial-time hierarchy collapses? By computing a multivalued function in deterministic polynomial-time we mean o...

A connectionist model made up of a combination of RBF networks is proposed the model decomposes multivalued dependencies into local single valued functions theory and applications are presented

We consider an approach to constructing a non-anticipating selection of a multivalued mapping; such a problem arises in control theory under conditions of uncertainty. The approach is called “unlocking of predicate” and consists in the reduction of finding the truth set of a predicate to searching fixed points of some mappings. Unlocking of predicate gives an extra opportunity to analyze the tr...