 Formal methods

Formal methods use mathematically defined models, specifications and reasoning techniques to describe and analyze systems. They include writing a formal specification, proving properties through formal verification, exploring a finite model by model checking and deriving information through static program analysis. A method's guarantee is relative to its model and assumptions.

For example, a loop summing an array can maintain the invariant that the current accumulator equals the sum of the entries already visited. Initialization, preservation by one iteration and the exit condition establish the returned sum; a separate termination argument shows that an answer is reached. Arithmetic and array bounds must be specified, since a proof using unbounded integers need not describe overflowing machine arithmetic.^[ref]

Formal methods are mathematical techniques and tools used for specifying, developing, and verifying software and hardware systems. These methods provide a rigorous framework for ensuring that systems meet their intended requirements and behave correctly. They are particularly useful in safety-critical applications, such as aerospace, automotive, medical devices, and telecommunications, where failures can have severe consequences. Key aspects of formal methods include: 1. **Mathematical Specification**: Formal methods use mathematical logic to create precise specifications of system behavior.