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Time-space lower bounds for satisfiability

Lance Fortnow, Richard Lipton, Dieter van Melkebeek, Anastasios Viglas
2005 Journal of the ACM  
We establish the first polynomial time-space lower bounds for satisfiability on general models of computation.  ...  We also use that paradigm to prove time-space lower bounds for languages higher up in the polynomial-time hierarchy.  ...  He is grateful to Steve Cook for bringing him into contact with Iannis Tourlakis.  ... 
doi:10.1145/1101821.1101822 fatcat:thy577mqmne6xcpufkwvhqi7ee

A time lower bound for satisfiability

Dieter van Melkebeek, Ran Raz
2005 Theoretical Computer Science  
For conondeterministic machines, we obtain a similar lower bound for any a such that a 3 < 1 + a/(d + 1). The same bounds apply to almost all natural NP-complete problems known.  ...  We show that a deterministic Turing machine with one d-dimensional work tape and random access to the input cannot solve satisfiability in time n a for a < √ (d + 2)/(d + 1).  ...  Acknowledgements We would like to thank Ravi Kannan, Rahul Santhanam, and the anonymous ICALP referees for helpful discussions, pointers to the literature, and other suggestions.  ... 
doi:10.1016/j.tcs.2005.09.020 fatcat:2zbggupixjgsvd5fxcywgliopu

A Time Lower Bound for Satisfiability [chapter]

Dieter van Melkebeek, Ran Raz
2004 Lecture Notes in Computer Science  
For conondeterministic machines, we obtain a similar lower bound for any a such that a 3 < 1 + a/(d + 1). The same bounds apply to almost all natural NP-complete problems known.  ...  We show that a deterministic Turing machine with one d-dimensional work tape and random access to the input cannot solve satisfiability in time n a for a < (d + 2)/(d + 1).  ...  Acknowledgments We would like to thank Ravi Kannan, Rahul Santhanam, and the anonymous ICALP referees for helpful discussions, pointers to the literature, and other suggestions.  ... 
doi:10.1007/978-3-540-27836-8_81 fatcat:4wfv4lejlngonj65wb7qkovr4i

Time‐Space Lower Bounds for the Polynomial‐Time Hierarchy on Randomized Machines

Scott Diehl, Dieter van Melkebeek
2006 SIAM journal on computing (Print)  
We establish the first polynomial-strength time-space lower bounds for problems in the linear-time hierarchy on randomized machines with bounded two-sided error.  ...  error in time n c and space n d .  ...  Acknowledgements We would like to thank Bess Berg and the anonymous referees for helpful comments.  ... 
doi:10.1137/050642228 fatcat:eduldhxm4fhvpmteetwfe73bka

A Survey of Lower Bounds for Satisfiability and Related Problems

Dieter van Melkebeek
2006 Foundations and Trends® in Theoretical Computer Science  
In this article we survey the known lower bounds for the time and space complexity of satisfiability and closely related problems on deterministic, randomized, and quantum models with random access.  ...  It is widely believed to be intractable, and yet till recently even a linear-time, logarithmic-space algorithm for satisfiability was not ruled out.  ...  Acknowledgments I would like to thank Madhu Sudan for the opportunity and incentive to write this survey, James Finlay for his patience while I was writing it, all my coauthors for their collaboration  ... 
doi:10.1561/0400000012 fatcat:vsdohimqr5a5zlbat3l37uwdem

Time-Space Lower Bounds for the Polynomial-Time Hierarchy on Randomized Machines [chapter]

Scott Diehl, Dieter van Melkebeek
2005 Lecture Notes in Computer Science  
Our lower bounds for space-bounded alternating linear time require a stronger diagonalization result which is both time-and space-sensitive. Lemma 6 ([9]).  ...  We establish the first polynomial-strength time-space lower bounds for problems in the lineartime hierarchy on randomized machines with two-sided error.  ...  We are grateful to Emanuele Viola for pushing us to optimize the space parameter in Theorems 1 and 2.  ... 
doi:10.1007/11523468_79 fatcat:tu7eceadn5flpcszt37wg7tzwu

Quadratic Time-Space Lower Bounds for Computing Natural Functions with a Random Oracle

Dylan M. McKay, Richard Ryan Williams, Michael Wagner
2018 Innovations in Theoretical Computer Science  
Note it is a major open problem to prove a time-space product lower bound of n 2−o(1) for the decision version of SAT, or even for the decision problem Majority-SAT.  ...  As our lower bounds are based on R-way branching programs, they hold for any reasonable model of computation (e.g. log-word RAMs and multitape Turing machines).  ...  Acknowledgements We thank the anonymous reviewers for helpful comments. 1 Parts of this work were performed while visiting the Simons Institute for the Theory of Computing and the EECS department at UC  ... 
doi:10.4230/lipics.itcs.2019.56 dblp:conf/innovations/McKayW19 fatcat:prlyjqud5vgujafxl7vtbkaco4

On the Fine Grained Complexity of Finite Automata Non-emptiness of Intersection [chapter]

Mateus de Oliveira Oliveira, Michael Wehar
2020 Lecture Notes in Computer Science  
This consequence strengthens the existing conditional lower bounds for k-DFA-NEI and implies new non-uniform circuit lower bounds.  ...  of nondeterministic linear space bounded computations.  ...  Further, this last result is in a similar spirit as conditional lower bounds for weighted satisfiability problems from [8] [9] [10] .  ... 
doi:10.1007/978-3-030-48516-0_6 fatcat:ixsbtp5aereifa7yn5hv5gqvne

An improved time-space lower bound for tautologies

Scott Diehl, Dieter van Melkebeek, Ryan Williams
2010 Journal of combinatorial optimization  
In particular, for every d < 3 √ 4 there exists a positive e such that tautologies cannot be decided by a nondeterministic algorithm that runs in time n d and space n e .  ...  a nondeterministic algorithm that runs in time n d and space n e .  ...  Acknowledgements The authors would like to thank an anonymous referee for a very careful reading of the manuscript and for helpful suggestions.  ... 
doi:10.1007/s10878-009-9286-x fatcat:a5uvcnupdfahblwqqexbxeitve

An Improved Time-Space Lower Bound for Tautologies [chapter]

Scott Diehl, Dieter van Melkebeek, Ryan Williams
2009 Lecture Notes in Computer Science  
In particular, for every d < 3 √ 4 there exists a positive e such that tautologies cannot be decided by a nondeterministic algorithm that runs in time n d and space n e .  ...  a nondeterministic algorithm that runs in time n d and space n e .  ...  Acknowledgements The authors would like to thank an anonymous referee for a very careful reading of the manuscript and for helpful suggestions.  ... 
doi:10.1007/978-3-642-02882-3_43 fatcat:wf6u5phizbg6bifoh4hsstsk2a

Space Complexity in Polynomial Calculus

Yuval Filmus, Massimo Lauria, Jakob Nordström, Noga Ron-Zewi, Neil Thapen
2015 SIAM journal on computing (Print)  
For the polynomial calculus proof system, the only previously known space lower bound is for CNF formulas of unbounded width in [Alekhnovich et al. '02], where the lower bound is smaller than the initial  ...  lower bound in PCR for these formulas as well. 3) We prove an Ω(n) space lower bound in PC for the canonical 3-CNF version of the pigeonhole principle formulas PHP m n with m pigeons and n holes, and  ...  PCR space lower bounds for specially crafted 4-CNF formulas, we still do not know any lower bounds for 3-CNF formulas.  ... 
doi:10.1137/120895950 fatcat:vzsfnttcf5gnppg7vz2ij3hmvm

Space Complexity in Polynomial Calculus

Yuval Filmus, Massimo Lauria, Jakob Nordstrom, Neil Thapen, Noga Ron-Zewi
2012 2012 IEEE 27th Conference on Computational Complexity  
For the polynomial calculus proof system, the only previously known space lower bound is for CNF formulas of unbounded width in [Alekhnovich et al. '02], where the lower bound is smaller than the initial  ...  lower bound in PCR for these formulas as well. 3) We prove an Ω(n) space lower bound in PC for the canonical 3-CNF version of the pigeonhole principle formulas PHP m n with m pigeons and n holes, and  ...  PCR space lower bounds for specially crafted 4-CNF formulas, we still do not know any lower bounds for 3-CNF formulas.  ... 
doi:10.1109/ccc.2012.27 dblp:conf/coco/FilmusLNTR12 fatcat:qmcbbck3fbgqhjoe5h4re3k6sm

Unitary signal constellations for differential space-time modulation with two transmit antennas: parametric codes, optimal designs, and bounds

Xue-Bin Liang, Xiang-Gen Xia
2002 IEEE Transactions on Information Theory  
For the practical success of differential space-time modulation, it has been shown critical to design unitary space-time signal constellations with large diversity product which is a primary property for  ...  Furthermore, by making use of the existing results in sphere packing and spherical codes, we provide several upper and lower bounds on the largest possible diversity Manuscript product and the largest  ...  Moreover, the upper and lower bounds on were generally given in terms of [5] , where satisfying , or equivalently, satisfying .  ... 
doi:10.1109/tit.2002.800498 fatcat:5cardfeuvbgzrnrcpobb5umnyu

Improving Exhaustive Search Implies Superpolynomial Lower Bounds

Ryan Williams
2013 SIAM journal on computing (Print)  
We also prove unconditional superpolynomial time-space lower bounds for improving on exhaustive search: there is a problem verifiable with k(n) length witnesses in O(n a ) time (for some a and some function  ...  While such problems can always be solved by exhaustive search in O(2 k(n) n a ) time and O(k(n) + n a ) space, we can prove a superpolynomial lower bound in the parameter k(n) when space usage is restricted  ...  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  
We also prove unconditional superpolynomial time-space lower bounds for improving on exhaustive search: there is a problem verifiable with k(n) length witnesses in O(n a ) time (for some a and some function  ...  While such problems can always be solved by exhaustive search in O(2 k(n) n a ) time and O(k(n) + n a ) space, we can prove a superpolynomial lower bound in the parameter k(n) when space usage is restricted  ...  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
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