Carnegie Mellon University

17-651 Models of Software Systems

Models of Software Systems is a 12 unit full semester course.

Scientific foundations for software engineering depend on the use of precise, abstract models for characterizing and reasoning about properties of software systems. This course considers many of the standard models for representing sequential and concurrent systems, such as state machines, algebras, and traces. It shows how different logics can be used to specify properties of software systems, such as functional correctness, deadlock freedom, and internal consistency. Concepts such as composition mechanisms, abstraction relations, invariants, non-determinism, inductive definitions and denotational descriptions are recurrent themes throughout the course. This course provides the formal foundations for the other core courses. Notations are not emphasized, although some are introduced for concreteness. Examples are drawn from software applications.

More course details can be found in the Models of Software Systems syllabus.

After completing this course, students will:

  • understand the strengths and weaknesses of certain models and logics including state machines, algebraic and process models, and temporal logic;
  • be able to select and describe appropriate abstract formal models for certain classes of systems, describe abstraction relations between different levels of description, and reason about the correctness of refinements;
  • capably prove elementary properties about systems described by the models introduced in the course.


  • Undergraduate discrete math including first-order logic, sets, functions, relations, proof techniques (such as induction).