Formal methods are mathematically based techniques for specifying, designing, and verifying software systems. Formal specifications precisely state what software should do without describing how. Formal verification rigorously proves an algorithm's correctness against a specification using logical rules. While formal methods reduce errors, the cost of full formalization is often prohibitive for industry; lightweight formal methods employing partial specification and focused analysis are alternatives.

1. Introduction to Formal Methods By : Hend Muhammad Rizk 61570 CS-303

2. What are formal methods? Formal methods are a mathematically based techniques and tools for the specification, design and verification of software systems .

3. Formal methods can be useful in : 1-Articulating, and representing requirements . 2-Specifying software : developing a precise statement of what the software is to do . 3-Software design . Data refinement involves state machine specification, abstraction functions, and simulation proofs .

4. 4-Coding verification . 5-Enhancing early error detection . 6-Developing safe, reliable, secure software - intensive systems .

5. The overall effect of the use of formal techniques on time, cost ,and quality :

6. Formal Specification Methods : Formal specifications . Formal Proofs . Model Checking . Abstraction .

7. Formal specification The specifications used in formal methods are well - formed statements which describe what some software should do , “ not necessarily how” in a language defined by a mathematical logic . This languages called “specification languages”

8. Properties of Formal Specifications : Unambiguous . Consistency . Completeness . Inference .

9. Formal Specification Languages : A formal specification language consists of : 1- Syntax — the notation . 2- Semantics — the specifiable objects . 3- Relation defining which objects satisfy which notations .

10. Basic Specification Language Types : 1- Axiomatic specifications : defines operations by logical assertions . 2- Abstract model specifications : defines operations in terms of a well - defined math model .

11. 3- Algebraic specifications : defines operations by collections of equivalence relations . 4- Temporal logic specifications : defines operations in terms of order of execution and timing . 5- Concurrent specifications : defines operations in terms of simultaneously occurring events .

12. Formal verification Formal verifications are rigorous deductions in logic ( i . e . each step follows from a rule of inference and hence can be checked by a mechanical process .)

13. Formal verification can also be defined to be the act of proving or disproving the correctness of some algorithm in a system with respect to a certain formal specification .

14. The cost of applying this methods is very high To make analysis economically feasible, the cost of specification must be dramatically reduced, and the analysis itself must be automated .

15. the cost of specification alone is often beyond a project's budget . Industry will have no reason to adopt formal methods until the benefits of formalization can be obtained immediately .

16. makeing full formalization is a difficult and expensive task . As an alternative, various lightweight formal methods, which emphasize partial specification and focused application, have been proposed .

17. Conclusions : Formal methods are : a mathematically based techniques and tools for the specification, design and verification of software systems . Formal specifications are : well - formed statements which describe what some software should do .

18. Formal verifications are : the act of proving or disproving the correctness of some algorithm in a system . formal methods cannot guarantee the completeness of a specifications .

19. Thanks for listening