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Time-space lower bounds for satisfiability
2005
Journal of the ACM
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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
2005
Theoretical Computer Science
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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]
2004
Lecture Notes in Computer Science
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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
2006
SIAM journal on computing (Print)
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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
2006
Foundations and Trends® in Theoretical Computer Science
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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]
2005
Lecture Notes in Computer Science
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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
2018
Innovations in Theoretical Computer Science
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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]
2020
Lecture Notes in Computer Science
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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
2010
Journal of combinatorial optimization
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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]
2009
Lecture Notes in Computer Science
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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
2015
SIAM journal on computing (Print)
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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
2012
2012 IEEE 27th Conference on Computational Complexity
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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
2002
IEEE Transactions on Information Theory
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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
2013
SIAM journal on computing (Print)
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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
2010
Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10
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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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