Formal verification

In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of a system with respect to a certain formal specification or property, using formal methods of mathematics.

Explanation

Software testing alone cannot prove that a system does not have a certain defect. Neither can it prove that it does have a certain property. Only the process of formal verification can prove that a system does not have a certain defect or does have a certain property. It is impossible to prove or test that a system has "no defect" since it is impossible to formally specify what "no defect" means. All that can be done is prove that a system does not have any of the defects that can be thought of, and has all of the properties that together make it functional and useful.

Usage

Formal verification can be used for example for systems such as cryptographic protocols, combinatorial circuits, digital circuits with internal memory, and software expressed as source code.

The verification of these systems is done by providing a formal proof on an abstract mathematical model of the system, the correspondence between the mathematical model and the nature of the system being otherwise known by construction. Examples of mathematical objects often used to model systems are: finite state machines, labelled transition systems, Petri nets, timed automata, hybrid automata, process algebra, formal semantics of programming languages such as operational semantics, denotational semantics, Hoare's logic.

Approaches to formal verification

There are roughly two approaches to formal verification.

The first approach is model checking, which consists of a systematically exhaustive exploration of the mathematical model (this is only possible for a model that is finite). Usually this consists of exploring all states and transitions in the model, by using smart and domain-specific abstraction techniques to consider whole groups of states in a single operation and reduce computing time. Implementation techniques include state space enumeration, symbolic state space enumeration, abstract interpretation, abstraction refinement.

The second approach is logical inference. It consists of using a formal version of mathematical reasoning about the system, usually using theorem proving software such as the HOL theorem prover or Isabelle theorem prover. This is usually only partially automated and is driven by the user's understanding of the system to validate.

The properties to be verified are often described in temporal logics, such as linear temporal logic (LTL) or computational tree logic (CTL).

Validation and Verification

Verification is one aspect of testing a product's fitness for purpose. Validation is the complementary aspect. Often one refers to the overall checking process as V & V.

Validation: "Are we building the right product?", i.e., does the product do what the user really requires?
Verification: "Are we building the product right?", i.e., does the product conform to the specifications?

The verification process consists of static and dynamic parts. E.g., for a software product one can inspect the source code (static) and run against specific test cases (dynamic). Validation usually can only be done dynamically, i.e., the product is tested by putting it through typical usages and atypical usages ("Can we break it?").

Program verification

Program verification is the process of formally proving that a computer program does exactly what is stated in the program specification it was written to realize. This is a type of formal verification which is specifically aimed at verifying the code itself, not an abstract model of the program.

For functional programming languages, some programs can be verified by equational reasoning, usually together with induction. Code in an imperative language could be proved correct by use of Hoare logic.

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Explanation

Usage

Approaches to formal verification

Validation and Verification

Program verification

See also