Algorithmics of Checking Whether a Mapping Is Injective, Surjective, and/or Bijective

Authors

E. Cabral Balreira, Trinity UniversityFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

4-2012

Comments

Technical Report: UTEP-CS-12-15

To appear in Proceedings of the Fifth International Workshop on Constraint Programming and Decision Making CoProD'12, Novosibirsk, Russia, September 23, 2012.

Abstract

In many situations, we would like to check whether an algorithmically given mapping f:A --> B is injective, surjective, and/or bijective. These properties have a practical meaning: injectivity means that the events of the action f can be, in principle, reversed, while surjectivity means that every state b from the set B can appear as a result of the corresponding action. In this paper, we discuss when algorithms are possible for checking these properties.