Interval arithmetic is an efficient model for controlling errors in numerical calculation and can be used to solve problems that cannot be effectively solved by floating point arithmetic. However, since an interval is classically represented by two numbers, lower and upper endpoints, it is obvious that performing arithmetic operations on interval need high computational time and space. A flexible interval representation system, where an interval can be represented as one string, was proposed in order to handle such a problem. Serial fundamental arithmetic operations (addition, subtraction, multiplication and division) are proved to be computable in this system. In this paper, we are interested in parallel addition and subtraction operations. We introduced a novel flexible digit-set in order to increase redundancy of the system. We demonstrate that parallel addition and subtraction can be realized by introducing addition and subtraction algorithms for flexible interval representation system together with the proof.
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