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- W2079232283 abstract "Let E be the set of all simple arithmetic expressions of the form E ( x ) = xT l … T k where x is a nonnegative integer variable and each T i is a multiplication or integer division by a positive integer constant. We investigate the complexity of the inequivalence and the bounded inequivalence problems for expressions in E . (The bounded inequivalence problem is the problem of deciding for arbitrary expressions E 1 ( x ) and E 2 ( x ) and a positive integer l whether or not E 1 ( x ) ≠ E 2 ( x ) for some nonnegative integer x < l . If l = ∞, i.e., there is no upper bound on x , the problem becomes the inequivalence problem.) We show that the inequivalence problem (or equivalently, the equivalence problem) for a large subclass of E is decidable in polynomial time. Whether or not the problem is decidable in polynomial time for the full class E remains open. We also show that the bounded inequivalence problem is NP-complete even if the divisors are restricted to be equal to 2. This last result can be used to sharpen some known NP-completeness results in the literature. Note that if division is rational division, all problems are trivially decidable in polynomial time." @default.
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- W2079232283 date "1982-07-01" @default.
- W2079232283 modified "2023-09-26" @default.
- W2079232283 title "On the complexity of simple arithmetic expressions" @default.
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- W2079232283 doi "https://doi.org/10.1016/0304-3975(82)90012-3" @default.
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