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dc.contributor.authorSalamon, András Z.
dc.contributor.authorWehar, Michael
dc.identifier.citationSalamon , A Z & Wehar , M 2023 , ' Effective guessing has unlikely consequences ' , Theory of Computing Systems , vol. 67 , pp. 548-568 .
dc.identifier.otherORCID: /0000-0002-1415-9712/work/132214028
dc.descriptionFunding: EPSRC Grant number EP/P015638/1.en
dc.description.abstractA classic result of Paul, Pippenger, Szemeredi and Trotter states that DTIME(n) ⊊ NTIME(n). The natural question then arises: could the inclusion DTIME(t (n)) ⊆ NTIME(n) hold for some superlinear time-constructible function t(n)? If such a function t(n) does exist, then there also exist effective nondeterministic guessing strategies to speed up deterministic computations. In this work, we prove limitations on the effectiveness of nondeterministic guessing to speed up deterministic computations by showing that the existence of effective nondeterministic guessing strategies would have unlikely consequences. In particular, we show that if a subpolynomial amount of nondeterministic guessing could be used to speed up deterministic computation by a polynomial factor, then P ⊊ NTIME(n). Furthermore, even achieving a logarithmic speedup at the cost of making every step nondeterministic would show that SAT ∈ NTIME(n) under appropriate encodings. Of possibly independent interest, under such encodings we also show that SAT can be decided in O(n log n) steps on a nondeterministic multitape Turing machine, improving on the well-known O(n(log n)c) bound for some constant but undetermined exponent c ≥ 1.
dc.relation.ispartofTheory of Computing Systemsen
dc.subjectComputational complexityen
dc.subjectStructural complexityen
dc.subjectLimited nondeterminismen
dc.subjectEffective guessingen
dc.subjectComplexity class containmentsen
dc.subjectQA75 Electronic computers. Computer scienceen
dc.titleEffective guessing has unlikely consequencesen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.contributor.institutionUniversity of St Andrews. School of Computer Scienceen
dc.description.statusPeer revieweden

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