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

Marco L. Carmosino, Jiawei Gao, Russell Impagliazzo, Ivan Mihajlin, Ramamohan Paturi, Stefan Schneider
2016 Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16  
NSETH 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  ... 
doi:10.1145/2840728.2840746 dblp:conf/innovations/CarmosinoGIMPS16 fatcat:qq7cmr4ehnbojapvajqgturwhm

Improving Exhaustive Search Implies Superpolynomial Lower Bounds

Ryan Williams
2013 SIAM journal on computing (Print)  
Since 2 n+1 /a(n + 1) = o(2 n ), we have a contradiction to 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.  ... 
doi:10.1137/10080703x fatcat:imqehe4hijbpfa354vudwpah5u

Improving exhaustive search implies superpolynomial lower bounds

Ryan Williams
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 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.  ... 
doi:10.1145/1806689.1806723 dblp:conf/stoc/Williams10 fatcat:27ullhp2ajbsnhblvpr5of4gii

Some Estimated Likelihoods for Computational Complexity [chapter]

R. Ryan Williams
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.  ... 
doi:10.1007/978-3-319-91908-9_2 fatcat:nptomjt6ojdjndevep7qsahvre

Effective guessing has unlikely consequences [article]

András Z. Salamon, Michael Wehar
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.  ... 
arXiv:2111.02138v1 fatcat:nuqs2mg5wnaqjog45sqedaftnm

Algorithms for Circuits and Circuits for Algorithms

Ryan Williams
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.  ... 
doi:10.1109/ccc.2014.33 dblp:conf/coco/Williams14 fatcat:t2irb2av2bcb5hzfi2dxkrsvqu

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

Thomas Bläsius, Tobias Friedrich, Julius Lischeid, Kitty Meeks, Martin Schirneck
2021 arXiv   pre-print
We also prove a conditional lower bound under 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.  ... 
arXiv:1805.01310v3 fatcat:zm626hj75javxjnay5it4ligse

On the (Non) NP-Hardness of Computing Circuit Complexity

Cody D. Murray, R. Ryan Williams, Marc Herbstritt
2015 Computational Complexity Conference  
We prove that 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.  ... 
doi:10.4230/lipics.ccc.2015.365 dblp:conf/coco/MurrayW15 fatcat:6fqqwrfaybfeho2yg4dccg75ay

On Nondeterministic Derandomization of Freivalds' Algorithm: Consequences, Avenues and Algorithmic Progress

Marvin Künnemann, Michael Wagner
2018 European Symposium on Algorithms  
in near-optimal 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  ... 
doi:10.4230/lipics.esa.2018.56 dblp:conf/esa/Kunnemann18 fatcat:mm5oyeslrjhorhaa7cxsryixmy

Strong ETH Breaks With Merlin and Arthur: Short Non-Interactive Proofs of Batch Evaluation [article]

Ryan Williams
2016 arXiv   pre-print
We point to some potential future directions 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.  ... 
arXiv:1601.04743v1 fatcat:my4lduyc3zdrrk5ewyeaub7j6u

A note on width-parameterized SAT: An exact machine-model characterization

Periklis A. Papakonstantinou
2009 Information Processing Letters  
Although pathwidth is 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.  ... 
doi:10.1016/j.ipl.2009.09.012 fatcat:kjbhlxplhrfhfgudicqpy4u2wq

Planning for Temporally Extended Goals in Pure-Past Linear Temporal Logic: A Polynomial Reduction to Standard Planning [article]

Giuseppe De Giacomo, Marco Favorito, Francesco Fuggitti
2022 arXiv   pre-print
deterministic 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) .  ... 
arXiv:2204.09960v3 fatcat:zh2gei2ayzeelmo6fd3h5xtr4u

A survey of complexity results for non-monotonic logics

Marco Cadoli, Marco Schaerf
1993 The Journal of Logic Programming  
This paper surveys 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.  ... 
doi:10.1016/0743-1066(93)90029-g fatcat:iewbxiclhbbwzeayv6esr2c5ei

Is the Standard Proof System for SAT P-Optimal? [chapter]

Johannes Köbler, Jochen Messner
2000 Lecture Notes in Computer Science  
By replacing 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]).  ... 
doi:10.1007/3-540-44450-5_29 fatcat:dzvqiuiz5zehlma4vfnmlhcwsa

Plan aggregation for strong cyclic planning in nondeterministic domains

Ron Alford, Ugur Kuter, Dana Nau, Robert P. Goldman
2014 Artificial Intelligence  
We describe a planning algorithm, NDP2, that finds 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.  ... 
doi:10.1016/j.artint.2014.07.007 fatcat:aazaffa2ivcf5j5insnutnlsuu
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