  Behavior Engineering (BE) provides a rigorous way to derive a formal
specification of a software system from the requirements written in natural
language. Its graphical specification language, Behavior Tree (BT), has been
used with success in industry to systematically translate large, complex, and
often erroneous requirements into an integrated model of the software system.
BE's process, the Behavior Modeling Process (BMP), allows requirements to be
translated into individual requirement BTs one at a time, which are then
integrated to form a holistic view of the system. The integrated BT then goes
through a series of modifications to construct a specification BT, which is
used for validation and verification. The BMP also addresses different types of
defects in the requirements throughout its process. However, BT itself is a
graphical modeling notation, and the types of integration relations, how they
correspond to particular issues, how they should be integrated and how to get
formal specification have not been clearly defined. As a result, the BMP is
informal, and provides guidelines to perform all these tasks on an ad-hoc
basis. In this paper, we first introduce a mathematical framework which defines
the graphical form of BTs which we use to define the integration relationships
of BTs and to formalize the integration strategy of the BMP. We then formulate
semi-automated requirements defects detection techniques by utilizing this
underlying mathematical framework, which may be extended to formalize the BMP,
develop change management framework for it, build techniques for round-trip
engineering and so on.
