  Context: Refactoring is the art of modifying the design of a system without
altering its behavior. The idea is to reorganize variables, classes and methods
to facilitate their future adaptations and comprehension. As the concept of
behavior preservation is fundamental for refactoring, several studies, using
formal verification, language transformation and dynamic analysis, have been
proposed to monitor the execution of refactoring operations and their impact on
the program semantics. However, there is no existing study that examines the
available behavior preservation strategies for each refactoring operation.
  Objective: This paper identifies behavior preservation approaches in the
research literature.
  Method: We conduct, in this paper, a systematic mapping study, to capture all
existing behavior preservation approaches that we classify based on several
criteria including their methodology, applicability, and their degree of
automation.
  Results: The results indicate that several behavior preservation approaches
have been proposed in the literature. The approaches vary between using
formalisms and techniques, developing automatic refactoring safety tools, and
performing a manual analysis of the source code.
  Conclusion: Our taxonomy reveals that there exist some types of refactoring
operations whose behavior preservation is under-researched. Our classification
also indicates that several possible strategies can be combined to better
detect any violation of the program semantics.
