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Nondeterministic Extensions of the Strong Exponential Time Hypothesis and Consequences for Non-reducibility

2016
*
Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16
*

NSETH

doi:10.1145/2840728.2840746
dblp:conf/innovations/CarmosinoGIMPS16
fatcat:qq7cmr4ehnbojapvajqgturwhm
*Nondeterministic**Strong**Exponential**Time**Hypothesis**For*every s > 0, there is a k such that k -SAT cannot be solved in co-*nondeterministic**time*2 (1−s)n Property X L 1 Det. Nondet. Co-Nondet. ... Outline*The*following problems have fast*nondeterministic**and*co-*nondeterministic*algorithms: Outline*The*following problems have fast*nondeterministic**and*co-*nondeterministic*algorithms: Max List*and*...##
###
Improving Exhaustive Search Implies Superpolynomial Lower Bounds

2013
*
SIAM journal on computing (Print)
*

Since 2 n+1 /a(n + 1) = o(2 n ), we have a contradiction to

doi:10.1137/10080703x
fatcat:imqehe4hijbpfa354vudwpah5u
*the**strong**nondeterministic**time*hierarchy theorem [SFM78, Zak83] . ... AC 0 circuits have constant depth*and*are comprised*of**AND*, OR, NOT gates, with unbounded fan-in*for*each gate. 5 Recall E NP is*the*class*of*languages recognized by an algorithm running in 2 O(n)*time*... Arvind, Andrew Drucker, Mike Fellows,*and*Rahul Santhanam*for*their valuable comments*and*corrections on a draft*of*this paper. ...##
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Improving exhaustive search implies superpolynomial lower bounds

2010
*
Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10
*

Since 2 n+1 /a(n + 1) = o(2 n ), we have a contradiction to

doi:10.1145/1806689.1806723
dblp:conf/stoc/Williams10
fatcat:27ullhp2ajbsnhblvpr5of4gii
*the**strong**nondeterministic**time*hierarchy theorem [SFM78, Zak83] . ... AC 0 circuits have constant depth*and*are comprised*of**AND*, OR, NOT gates, with unbounded fan-in*for*each gate. 5 Recall E NP is*the*class*of*languages recognized by an algorithm running in 2 O(n)*time*... Arvind, Andrew Drucker, Mike Fellows,*and*Rahul Santhanam*for*their valuable comments*and*corrections on a draft*of*this paper. ...##
###
Some Estimated Likelihoods for Computational Complexity
[chapter]

2019
*
Lecture Notes in Computer Science
*

*The*editors

*of*this LNCS volume asked me to speculate on open problems: out

*of*

*the*prominent conjectures in computational complexity, which

*of*them might be true,

*and*why? ... I hope

*the*reader is entertained. ... SETH:

*The*

*Strong*

*Exponential*

*Time*

*Hypothesis*Recall that SETH asserts that

*For*all δ < 1, there is k such that k-SAT on n variables is not in 2 δn

*time*. ...

##
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Effective guessing has unlikely consequences
[article]

2021
*
arXiv
*
pre-print

*The*natural question then arises: could DTIME(t(n)) be contained in NTIME(n)

*for*some superlinear

*time*-constructible function t(n)? ... 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 ...

*and*

*the*proof

*of*

*the*Linear Speedup Theorem

*for*

*nondeterministic*Turing machines provides an example where

*the*use

*of*additional

*nondeterministic*guesses leads to a faster simulation. ...

##
###
Algorithms for Circuits and Circuits for Algorithms

2014
*
2014 IEEE 29th Conference on Computational Complexity (CCC)
*

*For*instance,

*the*NEXP versus P/poly question asks whether

*nondeterministic*

*exponential*-

*time*algorithms can be simulated using

*non*-uniform circuit families

*of*polynomial size. ... Circuits

*for*algorithms refers to

*the*modeling

*of*uniform algorithms with

*non*-uniform circuit families (or proving such modeling is impossible). ... ACKNOWLEDGMENT

*The*author acknowledges support by

*the*Alfred P. Sloan foundation, Microsoft Research,

*and*

*the*NSF under grant CCF-1212372. ...

##
###
Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling
[article]

2021
*
arXiv
*
pre-print

We also prove a conditional lower bound under

arXiv:1805.01310v3
fatcat:zm626hj75javxjnay5it4ligse
*the**Strong**Exponential**Time**Hypothesis*, showing that this is close to optimal. ... We give an algorithm*for**the**extension*problem running in*time*O(m^|X|+1 n). ...*The*authors would like to thank Felix Naumann*and*Thorsten Papenbrock*for**the*many fruitful discussions about data profiling,*and*Erik Kohlros*for*conducting additional experiments. ...##
###
On the (Non) NP-Hardness of Computing Circuit Complexity

2015
*
Computational Complexity Conference
*

We prove that

doi:10.4230/lipics.ccc.2015.365
dblp:conf/coco/MurrayW15
fatcat:6fqqwrfaybfeho2yg4dccg75ay
*the*NP-hardness*of*MCSP under (logtime-uniform) AC0 reductions would imply extremely*strong*lower bounds: NP ⊂ P /poly*and*E ⊂ i.o. ... We also consider*the**nondeterministic*generalization*of*MCSP:*the**Nondeterministic*Minimum Circuit Size Problem (NMCSP), where one wishes to compute*the**nondeterministic*circuit complexity*of*a given function ... We're also grateful to Eric*for*providing a preprint*of*his work with Dhiraj Holden. ...##
###
On Nondeterministic Derandomization of Freivalds' Algorithm: Consequences, Avenues and Algorithmic Progress

2018
*
European Symposium on Algorithms
*

in near-optimal

doi:10.4230/lipics.esa.2018.56
dblp:conf/esa/Kunnemann18
fatcat:mm5oyeslrjhorhaa7cxsryixmy
*nondeterministic**time*Õ(n 2 ). ... We discuss*consequences**of*a positive or negative resolution*of*this problem*and*provide potential avenues towards resolving it. ... A*nondeterministic*derandomization, more precisely, a O(n 2−ε )-*time*verifier, would have interesting*consequences*[47] : it would refute*the**Nondeterministic**Strong**Exponential**Time**Hypothesis*posed ...##
###
Strong ETH Breaks With Merlin and Arthur: Short Non-Interactive Proofs of Batch Evaluation
[article]

2016
*
arXiv
*
pre-print

We point to some potential future directions

arXiv:1601.04743v1
fatcat:my4lduyc3zdrrk5ewyeaub7j6u
*for*refuting*the**Nondeterministic**Strong*ETH. ...*For*example, we obtain MA-proof systems that run in c^n*time*(*for*various c < 2)*for**the*Permanent, #Circuit-SAT*for*all sublinear-depth circuits, counting Hamiltonian cycles,*and*infeasibility*of*0-1 ... I thank Russell Impagliazzo*for*sending a draft*of*his paper (with coauthors) on NSETH, MASETH,*and*AMSETH,*and**for*discussions on*the*#SAT protocol. ...##
###
A note on width-parameterized SAT: An exact machine-model characterization

2009
*
Information Processing Letters
*

Although pathwidth is

doi:10.1016/j.ipl.2009.09.012
fatcat:kjbhlxplhrfhfgudicqpy4u2wq
*the*most restrictive among*the*studied width-parameterizations*of*SAT,*the*most*time*-efficient algorithms known*for*such SAT instances run in*time*2 Ω(w(n)) , even when*the*path-decomposition ... with at most r(n) passes over*the**nondeterministic*tape. ... I'd also like to thank Toniann Pitassi*for**the*helpful discussions,*and*Charles Rackoff*for**the*close attention to my work. ...##
###
Planning for Temporally Extended Goals in Pure-Past Linear Temporal Logic: A Polynomial Reduction to Standard Planning
[article]

2022
*
arXiv
*
pre-print

deterministic

arXiv:2204.09960v3
fatcat:zh2gei2ayzeelmo6fd3h5xtr4u
*and**nondeterministic*domains (FOND) remains*the*same as*for*classical reachability goals. ... We show*the*formal correctness*of**the*translation, its complexity,*and*its practical effectiveness through some comparative experiments. ... Hence,*the*conversion*of*ppltl formulas to their corresponding dfas is worst-case single*exponential**time*(vs. double*exponential**time**for*ltl f formulas) (De Giacomo et al., 2020) . ...##
###
A survey of complexity results for non-monotonic logics

1993
*
The Journal of Logic Programming
*

This paper surveys

doi:10.1016/0743-1066(93)90029-g
fatcat:iewbxiclhbbwzeayv6esr2c5ei
*the*main results appearing in*the*literature on*the*computational complexity*of**non*-monotonic inference tasks. ... We not only give results about*the*tractability/intractability*of**the*individual problems but we also analyze sources*of*complexity*and*explain intuitively*the*nature*of*easy/hard cases. ... an*exponential*number*of**times*. ...##
###
Is the Standard Proof System for SAT P-Optimal?
[chapter]

2000
*
Lecture Notes in Computer Science
*

By replacing

doi:10.1007/3-540-44450-5_29
fatcat:dzvqiuiz5zehlma4vfnmlhcwsa
*the*assumption*of**the*mere existence*of*a (p-)optimal proof system by*the*assumption that certain proof systems are (p-)optimal we obtain stronger*consequences*, namely collapse results*for*... We investigate*the*question whether there is a (p-)optimal proof system*for*SAT or*for*TAUT*and*its relation to completeness*and*collapse results*for**nondeterministic*function classes. ... double*exponential**time*are contained in deterministic double*exponential**time*; see 11]). ...##
###
Plan aggregation for strong cyclic planning in nondeterministic domains

2014
*
Artificial Intelligence
*

We describe a planning algorithm, NDP2, that finds

doi:10.1016/j.artint.2014.07.007
fatcat:aazaffa2ivcf5j5insnutnlsuu
*strong*-cyclic solutions to*nondeterministic*planning problems by using a classical planner to solve a sequence*of*classical planning problems. ... Which planner did better depended on three things:*the*amount*of*nondeterminism in*the*planning domain, domain characteristics that affected how well*the*abstraction techniques worked,*and*whether*the*...*Consequently*,*for**the*problems*of*sizes 15*and*21, there were few problems that NDP2 did not solve within*the**time*limit, even though MBP solved all 100 problems*of*each size. ...
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