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Short Propositional Refutations for Dense Random 3CNF Formulas
[article]
2011
arXiv
pre-print
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Random 3CNF formulas constitute an important distribution for measuring the average-case behavior of propositional proof systems. ...
In this paper we show that already standard propositional proof systems, within the hierarchy of Frege proofs, admit short refutations for random 3CNF formulas, for sufficiently large clause-to-variable ...
Acknowledgments We wish to thank Jan Krajíček for very helpful discussions concerning the topic of this paper and for commenting on an earlier manuscript and Emil Jeřabek and Neil Thapen for answering ...
arXiv:1101.3970v2
fatcat:ljar3wx6vjbmbkqdgn57uwrkqu
Short propositional refutations for dense random 3CNF formulas
2014
Annals of Pure and Applied Logic
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Random 3CNF formulas constitute an important distribution for measuring the average-case behavior of propositional proof systems. ...
In this paper we show that already standard propositional proof systems, within the hierarchy of Frege proofs, admit short refutations for random 3CNF formulas, for sufficiently large clause-to-variable ...
of our questions about theories of weak arithmetic and for many other insightful comments, and the anonymous reviewer who invested a lot of effort in reading the manuscript and providing us with many ...
doi:10.1016/j.apal.2014.08.001
fatcat:3z3cokqzqnamzphp6u4dr4pcpe
Complexity of propositional proofs under a promise
2010
ACM Transactions on Computational Logic
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We then investigate the complexity of such systems, obtaining an exponential separation in the average-case between resolution under different size promises: (i) Resolution has polynomial-size refutations ...
(ii) There are no sub-exponential size resolution refutations for random 3CNF formulas, when the promise is 2 δn (and the number of clauses is o(n 3/2 )), for any constant 0 < δ < 1. ...
We also wish to thank Jan Krajíček for commenting on an earlier version of this paper and Eli Ben-Sasson and Amnon Ta-Shma for useful correspondence and conversations. ...
doi:10.1145/1740582.1740586
fatcat:ehy3fl6bcze3ndcpckgl535dpq
Complexity of Propositional Proofs under a Promise
[article]
2007
arXiv
pre-print
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We then investigate the complexity of such systems, obtaining an exponential separation in the average-case between resolution under different size promises: 1. ...
There are no sub-exponential size resolution refutations for random 3CNF formulas, when the promise is 2^δ n (and the number of clauses is o(n^3/2)), for any constant 0<δ<1. ...
We wish to thank Jan Krajíček for commenting on an early version of this paper and Eli Ben-Sasson and Amnon Ta-Shma for useful correspondence and conversations. ...
arXiv:0707.4255v1
fatcat:5iigbvcyw5e5xp7g5z2leb23qa
Sparser Random 3SAT Refutation Algorithms and the Interpolation Problem
[article]
2014
arXiv
pre-print
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We formalize a combinatorial principle, called the 3XOR principle, due to Feige, Kim and Ofek (2006), as a family of unsatisfiable propositional formulas for which refutations of small size in any propositional ...
proof system that possesses the feasible interpolation property imply an efficient deterministic refutation algorithm for random 3SAT with n variables and Ω(n^1.4) clauses. ...
Thanks also to the anonymous reviewers of this paper who helped much in improving the exposition of this work. ...
arXiv:1305.0948v3
fatcat:eyybsdsry5brjgug67pkakimhi
Sparser Random 3-SAT Refutation Algorithms and the Interpolation Problem
[chapter]
2014
Lecture Notes in Computer Science
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We formalize a combinatorial principle, called the 3XOR principle, due to Feige, Kim and Ofek [14], as a family of unsatisfiable propositional formulas for which refutations of small size in any propositional ...
proof system that possesses the feasible interpolation property imply an efficient deterministic refutation algorithm for random 3SAT with n variables and Ω(n 1.4 ) clauses. ...
Acknowledgments I wish to thank Jan Krajíček for useful comments related to this work and Albert Atserias and Neil Thapen for useful related discussions. ...
doi:10.1007/978-3-662-43948-7_84
fatcat:jcna7uxo3bgpplvyhbmoabzlem
Average-Case Complexity
2006
Foundations and Trends® in Theoretical Computer Science
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While the relation between worst-case and average-case complexity for general NP problems remains open, there has been progress in understanding the relation between different "degrees" of average-case ...
We survey the average-case complexity of problems in NP. We discuss various notions of good-on-average algorithms, and present completeness results due to Impagliazzo and Levin. ...
Acknowledgments We thank Scott Aaronson, Jonathan Katz, Chris Moore and the anonymous referee for their helpful comments. ...
doi:10.1561/0400000004
fatcat:6emvwcgkinbgblhqzcdt7nzmou
Average-Case Complexity
[article]
2021
arXiv
pre-print
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While the relation between worst-case and average-case complexity for general NP problems remains open, there has been progress in understanding the relation between different "degrees" of average-case ...
We survey the average-case complexity of problems in NP. We discuss various notions of good-on-average algorithms, and present completeness results due to Impagliazzo and Levin. ...
Acknowledgements We thanks Scott Aaronson, Jonathan Katz, Chris Moore and the anonymous referee for their helpful comments. ...
arXiv:cs/0606037v3
fatcat:ishwc6ck2vhztpfb5z3bjywehi
Average-case Complexity
2008
2008 49th Annual IEEE Symposium on Foundations of Computer Science
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We survey the theory of average-case complexity, with a focus on problems in NP. ...
For the case of 3CNF, there is evidence suggesting that refuting random formulas is hard for m 3 (n) < n 3/2−ε for every ε > 0. ...
This short discussion anticipates the formal definition of one-way function and the difficulties in defining a robust notion of "average-case tractability" in Levin's theory of average-case complexity. ...
doi:10.1109/focs.2008.90
dblp:conf/focs/Trevisan08
fatcat:6rp35qbwpvhvjpzcxw4uufxg3m
Semialgebraic Proofs and Efficient Algorithm Design
2019
Foundations and Trends® in Theoretical Computer Science
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The authors would like to thank Ian Mertz for his suggestions on the presentation of the 3XOR lower bound in Section 5.1. ...
Finally, we are grateful to Paul Beame for correcting several historical remarks made in an earlier draft of this manuscript. ...
Recently there has been a surge of works for showing SoS lower bounds for average-case settings. ...
doi:10.1561/0400000086
fatcat:sotovlogzjfy7kxxloglpu5tym
Complexity of Propositional Proofs Under a Promise
[chapter]
Lecture Notes in Computer Science
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We then investigate the complexity of such systems, obtaining an exponential separation in the average-case between resolution under different size promises: (i) Resolution has polynomial-size refutations ...
(ii) There are no sub-exponential size resolution refutations for random 3CNF formulas, when the promise is 2 δn (and the number of clauses is o(n 3/2 )), for any constant 0 < δ < 1. ...
We also wish to thank Jan Krajíček for commenting on an earlier version of this paper and Eli Ben-Sasson and Amnon Ta-Shma for useful correspondence and conversations. ...
doi:10.1007/978-3-540-73420-8_27
fatcat:3w77gvjfg5aernsvrfc5uorxpq
A Resolution-Based Theorem Prover for $${\textsf {K}}_{n}^{}$$Kn: Architecture, Refinements, Strategies and Experiments
2018
Journal of automated reasoning
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In this paper we describe the implementation of K S P, a resolution-based prover for the basic multimodal logic K n . ...
We describe these options in detail and discuss their implications. We provide experiments comparing some of these options and comparing the prover with other provers for this logic. ...
In this case, a refutation for a set of clauses Φ is either a global refutation or a derivation Φ 0 , . . . , Φ k , k ∈ N, where * : start ⇒ false ∈ Φ k . ...
doi:10.1007/s10817-018-09503-x
fatcat:rhvht7pvnnfp3ggvvaq6d6whdm
Polylogarithmic Cuts in Models of V0
2013
Logical Methods in Computer Science
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As an interesting observation we also obtain an average case separation of Resolution from AC0-Frege by applying a recent result with Tzameret. ...
We can then exploit our result in Proof Complexity to observe that Frege proof systems can be sub exponentially simulated by bounded depth Frege proof systems. ...
Thus, this yields an average case separation between Resolution and TC 0 -Frege. We can now extend this result to an average case separation between Resolution and AC 0 -Frege as follows. Proof. ...
doi:10.2168/lmcs-9(1:16)2013
fatcat:3jfrecll2vaejmnhew5iymzwx4
Small Clique Detection and Approximate Nash Equilibria
[chapter]
2009
Lecture Notes in Computer Science
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(2 + δ) log n in G n,1/2 in polynomial time for arbitrarily small δ > 0. ...
Recently, Hazan and Krauthgamer showed [12] that if, for a fixed small ε, an ε-best ε-approximate Nash equilibrium can be found in polynomial time in two-player games, then it is also possible to find ...
-The planted k-clique problem is (for certain values of k) related to the assumption that refuting low-density 3CNF formulas is hard on the average. ...
doi:10.1007/978-3-642-03685-9_50
fatcat:dv4xm3ewpvcebghe6f3p2zhkdi
Proof Complexity Lower Bounds from Algebraic Circuit Complexity
[article]
2016
pre-print
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We complement our lower bounds by giving short refutations of the previously-studied subset-sum axiom using IPS subsystems, allowing us to conclude strict separations between some of these subsystems. ...
This mimics an established research direction in the boolean setting for subsystems of Extended Frege proofs, where proof-lines are circuits from restricted boolean circuit classes. ...
in this work, as well as Avishay Tal for pointing out how Proposition B.1 implies an optimal functional lower bound for sparsity (Corollary B.3). ...
doi:10.4230/lipics.ccc.2016.32
arXiv:1606.05050v1
fatcat:t3i35lsfrnhcjmqcvcsuudgmwa
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