The uses of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing the appropriate mathematical analysis can contribute to the reliability and robustness of a design. They form an important theoretical underpinning for software engineering, especially where safety or security is involved. Formal methods are a useful adjunct to software testing since they help avoid errors and can also give a framework for testing. For industrial use, tool support is required. However, the high cost of using formal methods means that they are usually only used in the development of high-integrity and life-critical systems, where safety or security is of utmost importance. Formal methods are a particular kind of mathematically based technique for the specification, development, and verification of software and hardware systems.[46] The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing the appropriate mathematical analysis can contribute to the reliability and robustness of a design.