Formal Methods


As more complex computational systems are used within critical applications, it is becoming essential that these systems are formally specified.  Such specifications are used to give a precise and unambiguous description of the required system.  While this is clearly important in criticial systems such as industrial process management and air/spacecraft control, it is also becoming essential when applications involving E-commerce and mobile code are developed.  In addition, as computational systems become more complex in general, formal specification can allow us to define the key characteristics of systems in a clear way and so help the development process.

Formal specifications provide the basis for verification of properties of systems. While there are a number of ways in which this can be achieved, the model-checking approach is a practical and popular way to verify the temporal properties of finite-state systems. Indeed, such temporal verification is widely used within the design of critical parts of integrated circuits, has recently been used to verify parts of the control mechanism for one of NASA’s space probes, and is now beginning to be used to verify general Java programs.


1  State-Based Formal Methods (3.5 weeks):

  • classical logic
  • transformational systems
  • traditional approaches; Z specification; formal development cycle
  • case studies

2  Temporal Specification (3 weeks):

  • reactive systems
  • syntax and semantics of temporal logic; examples
  • temporal specification of reactive systems (safety, liveness, fairness)

3  Model Checking (3.5 weeks):

  • generating finite models;  analysis of a simple model checking algorithm
  • symbolic model checking;  overview of reduction methods
  • “on the fly”model checking; Spin and Promela
  • case study and practical verification of properties; advanced topics

Recommended Texts

"Using Z: Specification, Refinement and Proof" - J. Woodcock and J. Davies Prentice Hall, 1994.
"Model Checking" - E. M. Clarke, O. Grumberg, and D. Peled MIT Press, 2000.

Learning Outcomes

Upon completing this module, a student will:

  • understand the principles of standard formal methods, such as Z;
  • understand the basic notions of temporal logic and its use in relation to reactive systems;
  • understand the use of model checking techniques in the verification of reactive systems;
  • be aware of some of the current research issues related to formal methods.

Learning Strategy

Lectures and formative exercises.