Formal verification of multiplier circuits using computer algebra
نویسندگان
چکیده
Abstract Digital circuits are widely utilized in computers, because they provide models for various digital components and arithmetic operations. Arithmetic a subclass of that used to execute Boolean algebra. To avoid problems like the infamous Pentium FDIV bug, it is critical ensure correct. Formal verification can be determine correctness circuit with respect certain specification. However, circuits, particularly integer multipliers, represent challenge current methodologies and, reality, still necessitate significant amount manual labor. In my dissertation we examine develop automated reasoning approaches based on computer algebra, where word-level specification, modeled as polynomial, reduced by Gröbner basis inferred gate-level representation circuit. We precise formalization this process, which includes soundness completeness arguments adds mathematical background field. On practical side present an unique incremental column-wise algorithm preprocessing variable elimination simplify basis. Furthermore, algebraic proof calculus thesis allows obtaining certificates by-product order boost confidence outcomes tools. These efficiently verified independent checking
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ژورنال
عنوان ژورنال: IT
سال: 2022
ISSN: ['2196-7032', '1611-2776']
DOI: https://doi.org/10.1515/itit-2022-0039