Formal Mathematical Methods And Hardware Systems

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Literature Review Formal mathematical methods are system designs that utilize specific rigorous mathematical models in the production of software and hardware systems. The methods are unique in comparison with other methods for they utilize mathematical proof as a complement to system testing so as to ensure a perfect behavior. A formal approach to system designs ensures safety due to the complicated nature of systems. The use of formal verification schemes creates the difference between formal methods and other design systems. Hence, the primary principles of the system must be proven to be right before they are adopted. Extensive testing has been used for long in traditional system designs to ascertain behavior, but only finite conclusions are achieved. Testing only reveals situations where a system would not fail, but the behavior outside the testing scenario is not accounted for. If the result is positive after testing the theorem, then it remains true. An error in design is impossible to fix via formal verification but could help in identification of errors in reasoning which would otherwise be left unverified. The knowledge of mathematics results from proofs that consist of valid and certain conclusions. Verification of mathematical statements is not through experiments or social agreements but logical deductions from basic assumptions. The method assures that the knowledge has universal application since mapping a mathematical statement into physical reality holds
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