Relations Between Diagonalization, Proof Systems, and Complexity Gaps

dc.contributor.authorHartmanis, Jurisen_US
dc.date.accessioned2007-04-23T17:12:13Z
dc.date.available2007-04-23T17:12:13Z
dc.date.issued1977-06en_US
dc.description.abstractIn this paper we study diagonal processes over time-bounded computations of one-tape Turing machines by diagonalizing only over those machines for which there exist formal proofs that they operate in the given time bound. This replaces the traditional "clock" in resource bounded diagonalization by formal proofs about running times and establishes close relations between properties of proof systems and existence of sharp time bounds for one-tape Turing machine complexity classses. These diagonalization methods also show that the Gap Theorem for resource bounded computations can hold only for those complexity classes which differ from the corresponding provable complexity classes. Furthermore, we show that there exist recursive time bounds $T(n)$ such that the class of languages for which we can formally prove the existence of Turing machines which accept them in time $T(n)$ differs form the class of languages accepted by Turing machines for which we can prove formally that they run in time $T(n)$.en_US
dc.format.extent905080 bytes
dc.format.extent310074 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/postscript
dc.identifier.citationhttp://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR77-312en_US
dc.identifier.urihttps://hdl.handle.net/1813/6561
dc.language.isoen_USen_US
dc.publisherCornell Universityen_US
dc.subjectcomputer scienceen_US
dc.subjecttechnical reporten_US
dc.titleRelations Between Diagonalization, Proof Systems, and Complexity Gapsen_US
dc.typetechnical reporten_US
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