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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.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.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.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.description.peerreviewedPeer Reviewed
dc.rights.accessOpen Access
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

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