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- W2007014944 abstract "Deterministic summation modulo an arbitrary semigroup generalises the schemes of bounded summation and bounded product used to build up the class of elementary functions. As a special case it includes bounded first-order quantification over the integers. S n , as usual, is the group of permutations of [ n ] = {0, 1,…, n − 1}. B n stands for the monoid of all binary relations on [ n ], with relational composition as the semigroup operation. We show that in the presence of bounded quantification and boolean operations, deterministic summation modulo the group S n is already as powerful as deterministic summation modulo the monoid B n . The computational significance is that for certain machines (Bel'tyukov's stack register machines), the first corresponds to determinism, the second to nondeterminism." @default.
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- W2007014944 date "1997-02-01" @default.
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- W2007014944 title "Deterministic summation modulo Bn, the semigroup of binary relations on {0, 1,…, n − 1}" @default.
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- W2007014944 doi "https://doi.org/10.1016/s0304-3975(95)00245-6" @default.
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