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dc.contributor.authorChen, Yijia
dc.contributor.authorMuller, Moritz Martin
dc.contributor.authorYokoyama, Keita
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Ciències de la Computació
dc.date.accessioned2018-07-09T12:23:05Z
dc.date.available2018-07-09T12:23:05Z
dc.date.issued2018
dc.identifier.citationChen, Y., Müller, M., Yokoyama, K. A parameterized halting problem, the linear time hierarchy, and the MRDP theorem. A: Annual ACM/IEEE Symposium on Logic in Computer Science. "LICS '18: proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science". New York: Association for Computing Machinery (ACM), 2018, p. 235-244.
dc.identifier.isbn978-1-4503-5583-4
dc.identifier.urihttp://hdl.handle.net/2117/119165
dc.description.abstractThe complexity of the parameterized halting problem for nondeterministic Turing machines p-Halt is known to be related to the question of whether there are logics capturing various complexity classes [10]. Among others, if p-Halt is in para-AC0, the parameterized version of the circuit complexity class AC0, then AC0, or equivalently, (+, x)-invariant FO, has a logic. Although it is widely believed that p-Halt ∉. para-AC0, we show that the problem is hard to settle by establishing a connection to the question in classical complexity of whether NE ⊈ LINH. Here, LINH denotes the linear time hierarchy. On the other hand, we suggest an approach toward proving NE ⊈ LINH using bounded arithmetic. More specifically, we demonstrate that if the much celebrated MRDP (for Matiyasevich-Robinson-Davis-Putnam) theorem can be proved in a certain fragment of arithmetic, then NE ⊈ LINH. Interestingly, central to this result is a para-AC0 lower bound for the parameterized model-checking problem for FO on arithmetical structures.
dc.format.extent10 p.
dc.language.isoeng
dc.publisherAssociation for Computing Machinery (ACM)
dc.subjectÀrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat
dc.subject.lcshTuring machines
dc.subject.lcshComputational complexity
dc.titleA parameterized halting problem, the linear time hierarchy, and the MRDP theorem
dc.typeConference report
dc.subject.lemacTuring, Màquines de
dc.subject.lemacComplexitat computacional
dc.identifier.doi10.1145/3209108.3209155
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttps://dl.acm.org/citation.cfm?doid=3209108.3209155
dc.rights.accessOpen Access
local.identifier.drac23250476
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/648276/EU/A Unified Theory of Algorithmic Relaxations/AUTAR
local.citation.authorChen, Y.; Müller, M.; Yokoyama, K.
local.citation.contributorAnnual ACM/IEEE Symposium on Logic in Computer Science
local.citation.pubplaceNew York
local.citation.publicationNameLICS '18: proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science
local.citation.startingPage235
local.citation.endingPage244


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