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

In many situations, we would like to check whether an algorithmically given mapping f:A --\u3e 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