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Specification[ edit ] Formal methods may be used to give a description of the system to be developed, at whatever level s of detail desired.
This formal description can be used to guide further development activities see following sections ; additionally, it can be used to verify that the requirements for the system being developed have been completely and accurately specified. The need for formal specification systems has been noted for years.
Development[ edit ] Once a formal specification has been produced, the specification may be used as a guide while the concrete system is developed during the design process i. If the formal specification is in an operational semantics, the observed behavior of the concrete system can be compared with the behavior of the specification which itself should be executable or simulateable.
Additionally, the operational commands of the specification may be amenable to direct translation into executable code. If the formal specification is in an axiomatic semantics, the preconditions and postconditions of the specification may become assertions in the executable code.
Verification[ edit ] Once a formal specification has been developed, the specification may be used as the basis for proving properties of the specification and hopefully by inference the developed system. Human-directed proof[ edit ] Sometimes, the motivation for proving the correctness of a system is not the obvious need for reassurance of the correctness of the system, but a desire to understand the system better.
Consequently, some proofs of correctness are produced in the style of mathematical proof: A "good" proof is one which is readable and understandable by other human readers. Critics of such approaches point out that the ambiguity inherent in natural language allows errors to be undetected in such proofs; often, subtle errors can be present in the low-level details typically overlooked by such proofs.
Additionally, the work involved in producing such a good proof requires a high level of mathematical sophistication and expertise. Automated proof[ edit ] In contrast, there is increasing interest in producing proofs of correctness of such systems by automated means.
Automated techniques fall into three general categories: Automated theorem provingin which a system attempts to produce a formal proof from scratch, given a description of the system, a set of logical axioms, and a set of inference rules.
Model checkingin which a system verifies certain properties by means of an exhaustive search of all possible states that a system could enter during its execution.
Abstract interpretationin which a system verifies an over-approximation of a behavioural property of the program, using a fixpoint computation over a possibly complete lattice representing it. Some automated theorem provers require guidance as to which properties are "interesting" enough to pursue, while others work without human intervention.
Model checkers can quickly get bogged down in checking millions of uninteresting states if not given a sufficiently abstract model. Proponents of such systems argue that the results have greater mathematical certainty than human-produced proofs, since all the tedious details have been algorithmically verified.
The training required to use such systems is also less than that required to produce good mathematical proofs by hand, making the techniques accessible to a wider variety of practitioners.Apr 17, · In , North and South Korean leaders met at the "Peace House" in the border village of Panmunjom to sign an armistice ending hostilities in the Korean War.
Some 65 years later, a historic. If you would like to learn how to write a business report in English follow these tips and use the example report as a template on which to base your own business report.
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Writing a Formal Report A formal report provides information and presents recommendations based on that information. Examples include feasibility studies, position papers, research reports and problem solving reports. Each type of report has its own. In computer science, specifically software engineering and hardware engineering, formal methods are a particular kind of mathematically based technique for the specification, development and verification of software and hardware systems.
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