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In computational complexity theory , an integer circuit is a circuit model of computation in which inputs to the circuit are sets of integers and each gate of the circuit computes either a set operation or an arithmetic operation on its input sets .. computational complexity theory. computational complexity theory. circuit. circuit ( computer science ). model of computation. model of computation. set. set ( mathematics ). integer. integer. As an algorithmic problem , the possible questions are to find if a given integer is an element of the output node or if two circuits compute the same set .. set. set ( mathematics ). integer. integer. The decidability is still an open question , but there are results on restriction of thoses circuits .. Finding answers to some questions about this model could serve as a proof to many important mathematical conjectures , like Goldbach 's conjecture .. It is a natural extension of the circuits over sets of natural numbers when the considered set contains also negative integers , the definitions , which does not change , will not be repeated on this page .. set. set ( mathematics ). circuits over sets of natural numbers. circuits over sets of natural numbers. Only the differences will be mentioned .