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The Hard Problems Are Almost Everywhere For Random CNF-XOR Formulas

Jeffrey M. Dudek, Kuldeep S. Meel, Moshe Y. Vardi
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
CNF formulas known to be difficult for many SAT algorithms.  ...  In this paper, we present the first study of the runtime behavior of SAT solvers equipped with XOR-reasoning techniques on random CNF-XOR formulas.  ...  Although XOR-formulas can be solved individually in polynomial time (using Gaussian Elimination [Schaefer, 1978] ), XOR-formulas are empirically hard [Haanpää et al., 2006] for SAT solvers without equivalence  ... 
doi:10.24963/ijcai.2017/84 dblp:conf/ijcai/DudekMV17 fatcat:l3d4acceencftpib24rheu7n34

Efficient CNF Encoding of Boolean Cardinality Constraints [chapter]

Olivier Bailleux, Yacine Boufkhad
2003 Lecture Notes in Computer Science  
The proposed encoding is efficient with respect to unit propagation, which is implemented in almost all complete CNF satisfiability solvers.  ...  We prove the practical efficiency of this encoding on some problems arising in discrete tomography that involve many cardinality constraints.  ...  When e ¤ 0 or more generally in the case where all the b i 's are assigned a value, the problem is reduced to find an assignment to an XOR-CNF formula which is known to be polynomial.  ... 
doi:10.1007/978-3-540-45193-8_8 fatcat:ngg3acfuxja3rb6otkmg7abutq

Algorithms for selective enumeration of prime implicants

Luigi Palopoli, Fiora Pirri, Clara Pizzuti
1999 Artificial Intelligence  
When DNFs are considered and the problem is to find a prime implicant-and dually CNFs for prime implicates-it is easy to find an implicant but it is computationally difficult to find a prime implicant.  ...  Following the seminal papers [33,44] and [38] there are numerous algorithms recently proposed in the literature for computing prime implicants of formulae, among which the most relevant are those of [13  ...  Acknowledgement Many thanks to Mario Ettorre and Gennaro Giordano for helping us in developing the experiments and the anonymous referees for their precious suggestions that improved the presentation of  ... 
doi:10.1016/s0004-3702(99)00035-1 fatcat:r7q4rr74effepoykicogpmcuwa

Why are Proof Complexity Lower Bounds Hard?

Jan Pich, Rahul Santhanam
2019 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)  
The most famous of these is the P vs NP problem [14] , but there are numerous others such as the NP vs coNP problem, the PSPACE vs P problem, and the BPP vs P problem.  ...  system can efficiently establish hardness for most tautologies in the family.  ...  This implies that for every t ∈ ω(1), Q (and hence also Q) does not have p-size proofs of formulas lb P (φ n , n t ) for any sequence of tautologies φ n .  ... 
doi:10.1109/focs.2019.00080 dblp:conf/focs/PichS19 fatcat:4of45zsirzd6ldkebom27aeaqy

Lower Bounds and Hardness Amplification for Learning Shallow Monotone Formulas

Vitaly Feldman, Homin K. Lee, Rocco A. Servedio
2011 Journal of machine learning research  
This improved hardness is achieved using a general technique that we introduce for amplifying the hardness of "mildly hard" learning problems in either the PAC or SQ framework.  ...  In this paper we give the first unconditional lower bounds for learning problems of this sort by showing that polynomial-time algorithms cannot learn shallow monotone Boolean formulas under the uniform  ...  In particular, it rules out almost all known approaches to the learning problem, including the algorithms that rely solely on estimates of Fourier coefficients (which is the primary technique for learning  ... 
dblp:journals/jmlr/FeldmanLS11 fatcat:gboaogbqszcolhxx7k5xhvl5ya

Improved algebraic side-channel attack on AES

Mohamed Saied Emam Mohamed, Stanislav Bulygin, Michael Zohner, Annelie Heuser, Michael Walter, Johannes Buchmann
2012 2012 IEEE International Symposium on Hardware-Oriented Security and Trust  
Furthermore, we introduce a method for handling erroneous side-channel information, which allows our improved algebraic side-channel attack to partially escape the assumption of an error-free environment  ...  In this paper we present improvements of the algebraic side-channel analysis of the Advanced Encryption Standard (AES) proposed in the works of M. Renauld and F.-X. Standaert.  ...  The latter is a bottleneck for SAT, since XOR chains need exponentially large representation in CNF.  ... 
doi:10.1109/hst.2012.6224335 dblp:conf/host/MohamedBZHWB12 fatcat:n2jq7jyjt5dujerz2r3s5qlbyq

Improved algebraic side-channel attack on AES

Mohamed Saied Emam Mohamed, Stanislav Bulygin, Michael Zohner, Annelie Heuser, Michael Walter, Johannes Buchmann
2013 Journal of Cryptographic Engineering  
Furthermore, we introduce a method for handling erroneous side-channel information, which allows our improved algebraic side-channel attack to partially escape the assumption of an error-free environment  ...  In this paper we present improvements of the algebraic side-channel analysis of the Advanced Encryption Standard (AES) proposed in the works of M. Renauld and F.-X. Standaert.  ...  The latter is a bottleneck for SAT, since XOR chains need exponentially large representation in CNF.  ... 
doi:10.1007/s13389-013-0059-1 fatcat:skv4lmoerndnfhtaotdluydbqu

Optimality of size-degree tradeoffs for polynomial calculus

Nicola Galesi, Massimo Lauria
2010 ACM Transactions on Computational Logic  
Finally we show that random formulas in conjunctive normal form (3-CNF) are hard to refute in PCR k .  ...  We show a size hierarchy theorem for PCR k : PCR k is exponentially separated from PCR k+1 . This follows from the previous degree lower bound and from techniques developed for RES k .  ...  ACKNOWLEDGMENT We would like to thank the anonymous reviewers for the careful work and the several suggestions. Some of them were substantial and really improved this article.  ... 
doi:10.1145/1838552.1838556 fatcat:yhp2rsc4u5d5fgmgc2hhuc7j3i

Translation of Algorithmic Descriptions of Discrete Functions to SAT with Applications to Cryptanalysis Problems [article]

Alexander Semenov, Ilya Otpuschennikov, Irina Gribanova, Oleg Zaikin, Stepan Kochemazov
2020 arXiv   pre-print
We describe how cryptanalysis problems are reduced to SAT in such a way that it should be perceived as natural by the cryptographic community.  ...  In~the theoretical part of the paper we justify the main principles of general reduction to SAT for discrete functions from a class containing the majority of functions employed in cryptography.  ...  We are grateful to anonymous reviewers for their valuable comments that made it possible to significantly improve the quality of the present paper.  ... 
arXiv:1805.07239v5 fatcat:qrgcbbnag5a53davdbexvxbio4

Translation of Algorithmic Descriptions of Discrete Functions to SAT with Applications to Cryptanalysis Problems

Alexander Semenov, Ilya Otpuschennikov, Irina Gribanova, Oleg Zaikin, Stepan Kochemazov
2018 Logical Methods in Computer Science  
We describe how cryptanalysis problems are reduced to SAT in such a way that it should be perceived as natural by the cryptographic community.  ...  In~the theoretical part of the paper we justify the main principles of general reduction to SAT for discrete functions from a class containing the majority of functions employed in cryptography.  ...  We are grateful to anonymous reviewers for their valuable comments that made it possible to significantly improve the quality of the present paper.  ... 
doi:10.23638/lmcs-16(1:29)2020 fatcat:fuji3nvk75ggzb5535kccwdmbu

The approximate degree of DNF and CNF formulas

Alexander A. Sherstov
2022 Symposium on the Theory of Computing  
Furthermore, the DNF and CNF formulas that we construct are the simplest possible in that they have constant width.  ...  For any δ > 0, we construct DNF and CNF formulas of polynomial size with approximate degree Ω(n 1−δ ), essentially matching the trivial upper bound of n.  ...  The author is thankful to Justin Thaler and Mark Bun for useful comments on an earlier version of this paper.  ... 
doi:10.1145/3519935.3520000 dblp:conf/stoc/Sherstov22 fatcat:dkdsgrczrrdzlornrab5ya6hri

Understanding Space in Proof Complexity: Separations and Trade-offs via Substitutions [article]

Eli Ben-Sasson, Jakob Nordström
2010 arXiv   pre-print
Our collection of trade-offs cover almost the whole range of values for the space complexity of formulas, and most of the trade-offs are superpolynomial or even exponential and essentially tight.  ...  For current state-of-the-art DPLL SAT-solvers the two main bottlenecks are the amounts of time and memory used.  ...  to construct CNF formulas which are hard for different variants of resolution in various respects (see for example [AJPU02, BIW04, BEGJ00, BP03] and the sequence of papers [Nor09a, NH08, BN08] leading  ... 
arXiv:1008.1789v1 fatcat:ztijp7e4cbd3hchi6mxnucgr3u

Nondeterministic Direct Product Reductions and the Success Probability of SAT Solvers

Andrew Drucker
2013 2013 IEEE 54th Annual Symposium on Foundations of Computer Science  
As an application, we show that if NP is not in coNP/poly then, for every PPT algorithm attempting to produce satisfying assigments to Boolean formulas, there are infinitely many instances where the algorithm's  ...  In these theorems one assumes that a target function f is mildly hard against nondeterministic circuits, and concludes that the direct product f ⊗t is extremely hard against (only polynomially smaller)  ...  Acknowledgments I thank Avi Wigderson for helpful comments, and Robin Moser and Dominik Scheder for discussions of related questions.  ... 
doi:10.1109/focs.2013.84 dblp:conf/focs/Drucker13 fatcat:vcqxpllt3vedbacdlbsc5mwjdi

Hardness vs. randomness

N. Nisan, A. Wigderson
1988 [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science  
It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (e.g., P, NC, PSPACE, ...) using an arbitrary function that is hard for  ...  We believe that our results are very strong evidence that the gap between randomized and deterministic complexity is not large.  ...  Each of these computations can be converted to a CNF formula of size 2 nk over the oracle entries.  ... 
doi:10.1109/sfcs.1988.21916 dblp:conf/focs/NisanW88 fatcat:qtvqglf5yzbnbmjrapdz6rzc7a

Hardness vs randomness

Noam Nisan, Avi Wigderson
1994 Journal of computer and system sciences (Print)  
It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (e.g., P, NC, PSPACE, ...) using an arbitrary function that is hard for  ...  We believe that our results are very strong evidence that the gap between randomized and deterministic complexity is not large.  ...  Each of these computations can be converted to a CNF formula of size 2 nk over the oracle entries.  ... 
doi:10.1016/s0022-0000(05)80043-1 fatcat:vqgigqdbhzehzohlyvvhqga7cu
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