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Polynomial time ultrapowers and the consistency of circuit lower bounds
dc.contributor.author | Bydžovský, Jan |
dc.contributor.author | Muller, Moritz Martin |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Ciències de la Computació |
dc.date.accessioned | 2020-02-06T14:06:43Z |
dc.date.available | 2020-06-04T00:26:42Z |
dc.date.issued | 2020 |
dc.identifier.citation | Bydžovský, J.; Muller, M. Polynomial time ultrapowers and the consistency of circuit lower bounds. "Archive for mathematical logic", 2020, vol. 59, p. 127-147. |
dc.identifier.issn | 0933-5846 |
dc.identifier.other | https://www.cs.upc.edu/~moritz/pubs.html |
dc.identifier.uri | http://hdl.handle.net/2117/177012 |
dc.description.abstract | A polynomial time ultrapower is a structure given by the set of polynomial time computable functions modulo some ultrafilter. They model the universal theory ∀PV of all polynomial time functions. Generalizing a theorem of Hirschfeld (Israel J Math 20(2):111–126, 1975), we show that every countable model of ∀PV is isomorphic to an existentially closed substructure of a polynomial time ultrapower. Moreover, one can take a substructure of a special form, namely a limit polynomial time ultrapower in the classical sense of Keisler (in: Bergelson, V., Blass, A., Di Nasso, M., Jin, R. (eds.) Ultrafilters across mathematics, contemporary mathematics vol 530, pp 163–179. AMS, New York, 1963). Using a polynomial time ultrapower over a nonstandard Herbrand saturated model of ∀PV we show that ∀PV is consistent with a formal statement of a polynomial size circuit lower bound for a polynomial time computable function. This improves upon a recent result of Krajíček and Oliveira (Logical methods in computer science 13 (1:4), 2017). |
dc.format.extent | 21 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
dc.subject.lcsh | Polynomials |
dc.title | Polynomial time ultrapowers and the consistency of circuit lower bounds |
dc.type | Article |
dc.subject.lemac | Polinomis |
dc.identifier.doi | 10.1007/s00153-019-00681-y |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | https://link.springer.com/article/10.1007%2Fs00153-019-00681-y |
dc.rights.access | Open Access |
local.identifier.drac | 26839038 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/648276/EU/A Unified Theory of Algorithmic Relaxations/AUTAR |
local.citation.author | Bydžovský, J.; Muller, M. |
local.citation.publicationName | Archive for mathematical logic |
local.citation.volume | 59 |
local.citation.startingPage | 127 |
local.citation.endingPage | 147 |
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