Correctness (computer science) in the context of "Formal verification"

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⭐ Core Definition: Correctness (computer science)

In theoretical computer science, an algorithm is correct with respect to a specification if it behaves as specified. Best explored is functional correctness, which refers to the input–output behavior of the algorithm: for each input it produces an output satisfying the specification.

Within the latter notion, partial correctness, requiring that if an answer is returned it will be correct, is distinguished from total correctness, which additionally requires that an answer is eventually returned, i.e. the algorithm terminates. Correspondingly, to prove a program's total correctness, it is sufficient to prove its partial correctness, and its termination. The latter kind of proof (termination proof) can never be fully automated, since the halting problem is undecidable.

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👉 Correctness (computer science) in the context of 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. Formal verification is a key incentive for formal specification of systems, and is at the core of formal methods.It represents an important dimension of analysis and verification in electronic design automation and is one approach to software verification. The use of formal verification enables the highest Evaluation Assurance Level (EAL7) in the framework of common criteria for computer security certification.

Formal verification can be helpful in proving the correctness of systems such as: cryptographic protocols, combinational circuits, digital circuits with internal memory, and software expressed as source code in a programming language. Prominent examples of verified software systems include the CompCert verified C compiler and the seL4 high-assurance operating system kernel.

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Correctness (computer science) in the context of High-level programming language

A high-level programming language is a programming language with strong abstraction from the details of the computer. In contrast to low-level programming languages, it may use natural language elements, be easier to use, or may automate (or even hide entirely) significant areas of computing systems (e.g. memory management), making the process of developing a program simpler and more understandable than when using a lower-level language. The amount of abstraction provided defines how "high-level" a programming language is.

High-level refers to a level of abstraction from the hardware details of a processor inherent in machine and assembly code. Rather than dealing with registers, memory addresses, and call stacks, high-level languages deal with variables, arrays, objects, arithmetic and Boolean expressions, functions, loops, threads, locks, and other computer science abstractions, intended to facilitate correctness and maintainability. Unlike low-level assembly languages, high-level languages have few, if any, language elements that translate directly to a machine's native opcodes. Other features, such as string handling, object-oriented programming features, and file input/output, may also be provided. A high-level language allows for source code that is detached and separated from the machine details. That is, unlike low-level languages like assembly and machine code, high-level language code may result in data movements without the programmer's knowledge. Some control of what instructions to execute is handed to the compiler.

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