Iterated multiplication in VTC0

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00559081" target="_blank" >RIV/67985840:_____/22:00559081 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00153-021-00810-6" target="_blank" >https://doi.org/10.1007/s00153-021-00810-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00153-021-00810-6" target="_blank" >10.1007/s00153-021-00810-6</a>

Result language
angličtina
Original language name
Iterated multiplication in VTC0
Original language description
We show that VTC^0, the basic theory of bounded arithmetic corresponding to the complexity class TC^0, proves the IMUL axiom expressing the totality of iterated multiplication satisfying its recursive definition, by formalizing a suitable version of the TC^0 iterated multiplication algorithm by Hesse, Allender, and Barrington. As a consequence, VTC^0 can also prove the integer division axiom, and 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).
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA19-05497S" target="_blank" >GA19-05497S: Complexity of mathematical proofs and structures</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)