Formal methods involve mathematically-based techniques for specifying, developing, and verifying software and hardware systems. They use formal languages and logic to create unambiguous and precise descriptions that can be analyzed for consistency and correctness. Formal methods can be applied at different levels of rigor, from using some mathematical notation in English specifications to fully formal machine-checked proofs. While useful for complex, safety-critical systems, formal methods need not be applied to every component or phase of development in order to provide benefits like error detection.

1. Formal Methods in Software
Engineering

2. Formal methods for the problems
What is formal methods?
Formal methods = Formal Specification
+
Refinement
+
Formal Verification
2
Set theory, logics, algebra, etc.

3. What are Formal Methods?
• Definition
Mathematically based techniques for the specification,
development and verification of software and hardware
systems.
Can determine if:
– Specifications are satisfied.
– Implementation of a system is correct.
– Proving properties of a system.
Formal Methods in Software
Engineering
3

4. What are Formal Methods?
• Formal Language Specification
• Formal Methods are centred around a notation known as a
formal specification language.
Formal Semantics
– Mathematical base allows precise notions.
– Unambiguous.
– Allows consistency, correctness, specification and implementation to
be expressed.
Increase Human Understanding of Specified System.
&
Allow the possibility of formal reasoning and development.
Formal Methods in Software
Engineering
4

5. Three Levels of Formal Methods
Formal Methods in Software
Engineering
5
1. Requirements Only
2. No Analysis/Proof
3. Cost effective
1. Produce a
program in a more
formal manner
2. Use proofs of properties or
refinements from formal
specification
3. Costly
1. Use theorem prover
2. Fully formal machine-
checked proofs.
3. Expensive, hard and
often costly
4. Formally prove the entire
system.
LEVEL 0
Formal Specification
LEVEL 1
Formal Verification
LEVEL 2
Theorem Provers

6. Software Engineering and Formal
Methods
• Every Software engineering methodology is
based on a recommended development
process proceeding through several phases:
• Formal methods can:
• » Be a foundation for describing complex
systems
• » Be a foundation for reasoning about systems
• » Provide support for program development

7. What are Formal Methods?
• Techniques and tools based on mathematics and
formal logic
• application of discrete mathematics to software
engineering
• involves modeling and analysis
• with an underlying mathematically-precise notation
• Can assume various forms and levels of rigor
• least rigorous = Occasional mathematical notation embedded in English
specifications
• most rigorous = Fully formal specification languages with a precise semantics

8. Why Consider Formal Methods?
• Systems are increasingly
dependent on software
components
• Complexity of systems with
embedded software has
increased rapidly
• Maintaining reliability in
software-intensive systems is
very difficult

9. Why should we care?
• NIST (National Institute of Standards and
Technology) report
– software bugs cost $60 billion annually
• High profile incidents of systems failure
– Therac-25 radiation overdoses, 1985-87
– Northeast blackout, 2003
– Air traffic control, LA airport, 2004

10. Intellectual challenge
• Civil engineering
– Bridges don’t fail

11. Reliable Engineering

12. Intellectual challenge
• Civil engineering
– Bridges don’t fail
• Mechanical engineering
– Cars are reliable

14. Intellectual challenge
• Civil engineering
– Bridges don’t fail
• Mechanical engineering
– Cars are reliable
• Software engineering

16. Dijkstra Says
 You can only prove the presence of
a bug by Testing
 BUT!!!!
You can not prove the absence of a
Bug by Testing

17. Why is software hard?
• The human element
– Getting a consistent and complete set of
requirements is difficult
– Requirements often change
– Human beings use software in ways never
imagined by the designers

18. Why is software hard?
• The mathematical element
– Huge set of behaviors
– Nondeterminism
• External due to inputs
• Internal due to concurrency
– Even if the requirements are unchanging,
complete and formally specified, it is infeasible to
check all the behaviors

19. What to formalize?
• Models of requirements knowledge (so we
can reason about them)
• Specifications of requirements (so we can
document them precisely)
• Specifications of program design (so we can
verify correctness)

20. Formal Methods???

21. Using Formal Methods
• Selective use of Formal Methods
• Amount of formality can vary
• Need not build complete formal models
• Apply to the most critical pieces

22. Using Formal Methods
• Apply where existing analysis techniques are
weak Need not formally analyze every system
property E.g. check safety properties only
• Need not apply FM in every phase of
development E.g. use for modeling
requirements, but don’t formalize the system
design
• Can choose what level of abstraction (amount
of detail) to model