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• W3100360984 abstract "We show that $VTC^0$, the basic theory of bounded arithmetic corresponding to the complexity class $mathrm{TC}^0$, proves the $IMUL$ axiom expressing the totality of iterated multiplication satisfying its recursive definition, by formalizing a suitable version of the $mathrm{TC}^0$ iterated multiplication algorithm by Hesse, Allender, and Barrington. As a consequence, $VTC^0$ can also prove the integer division axiom, and (by results of Jeřabek) the RSUV-translation of induction and minimization for sharply bounded formulas. Similar consequences hold for the related theories $Delta^b_1$-$CR$ and $C^0_2$. As a side result, we also prove that there is a well-behaved $Delta_0$ definition of modular powering in $IDelta_0+WPHP(Delta_0)$." @default.
• W3100360984 created "2020-11-23" @default.
• W3100360984 creator A5091882087 @default.
• W3100360984 date "2020-11-05" @default.
• W3100360984 modified "2023-09-27" @default.
• W3100360984 title "Iterated multiplication in VTC 0 ." @default.
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• W3100360984 hasPublicationYear "2020" @default.
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