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Verifiable random functions with Boolean function constraints

Qianwen Wang, Rongquan Feng, Yan Zhu
2018 Science China Information Sciences  
The responsibility for scientific accuracy and content remains entirely with the authors.  ...  Dear editor, Verifiable random functions (VRFs) [1] are cryptographic functions that behaves like a random function for producing a random string y for any variant x, but also allows for efficient verification  ...  As a general example of CVRF, we present a practical construction, called a conditionally verifiable random function on Boolean function (CVRF-BF), to explore the common structure and method of CVRFs.  ... 
doi:10.1007/s11432-017-9228-6 fatcat:jl2o5bzd5fb7zpcwhex52k5hpy

The Nonapproximability of Non-Boolean Predicates

Lars Engebretsen
2004 SIAM Journal on Discrete Mathematics  
Constraint satisfaction programs where each constraint depends on a constant number of variables have the following property: The randomized algorithm that guesses an assignment uniformly at random satisfies  ...  We combine ideas from these two constructions and prove that there exists a large class of predicates on finite non-Boolean domains such that for predicates in the class, the naive randomized algorithm  ...  There also exists some predicates-such as linear equations mod p with two unknowns in every equation [1] , constraints on exactly two Boolean variables [9] , and a large class of so called regular constraints  ... 
doi:10.1137/s0895480100380458 fatcat:4sxew6ahejeghp6qedne4kkpmm

The SAT–UNSAT transition for random constraint satisfaction problems

Nadia Creignou, Hervé Daudé
2009 Discrete Mathematics  
We study threshold phenomena for a large class of random constraint satisfaction problems over finite domains.  ...  Our main contribution is a complete classification of the nature (sharp or coarse) of the SAT-UNSAT transition for random Boolean CSPs, which is based on easily decidable properties.  ...  Most of the works concern the satisfiability threshold effect associated with random formulas with special types of allowed constraints.  ... 
doi:10.1016/j.disc.2008.04.025 fatcat:n2o7cv7z4ba3jii43rudj4p2ci

The Non-approximability of Non-Boolean Predicates [chapter]

Lars Engebretsen
2001 Lecture Notes in Computer Science  
Constraint satisfaction programs where each constraint depends on a constant number of variables have the following property: The randomized algorithm that guesses an assignment uniformly at random satisfies  ...  We combine ideas from these two constructions and prove that there exists a large class of predicates on finite non-Boolean domains such that for predicates in the class, the naive randomized algorithm  ...  The final link in the chain is the observation that since our verifier uses only logarithmic randomness, we can form a CSP with polynomial size by enumerating the checked constraints for every possible  ... 
doi:10.1007/3-540-44666-4_27 fatcat:qdxsfwbw4vbafkooiapkg5e3pa

Candidate hard unique game

Subhash Khot, Dana Moshkovitz
2016 Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2016  
We propose a candidate reduction for ruling out polynomial-time algorithms for unique games, either under plausible complexity assumptions, or unconditionally for Lasserre semidefinite programs with a  ...  Thanks to everyone with whom we discussed related issues over the years. Thanks to Boaz Barak for suggestions that improved the presentation.  ...  In this problem one is given a set of boolean variables together with arity-k constraints over them.  ... 
doi:10.1145/2897518.2897531 dblp:conf/stoc/KhotM16 fatcat:urhpe5lwqfagpdrxotjgdbh5wu

Accuracy-Privacy Tradeoffs for Two-Party Differentially Private Protocols [chapter]

Vipul Goyal, Ilya Mironov, Omkant Pandey, Amit Sahai
2013 Lecture Notes in Computer Science  
Our work obtains general upper bounds on accuracy for differentially private two-party protocols computing any Boolean function.  ...  At the heart of our results is a new general geometric technique for obtaining non-trivial accuracy bounds for any Boolean functionality.  ...  The accuracy of a randomized Boolean mechanism M : {0, 1} n → {0, 1} with respect to a Boolean function f : {0, 1} n → {0, 1} Stronger notions of privacy are also interesting: for example, where symbols  ... 
doi:10.1007/978-3-642-40041-4_17 fatcat:lcdc2d26snhmffyc727qukprda

Expected number of locally maximal solutions for random Boolean CSPs

Nadia Creignou, Hervé Daudé, Olivier Dubois
2007 Discrete Mathematics & Theoretical Computer Science  
International audience For a large number of random Boolean constraint satisfaction problems, such as random $k$-SAT, we study how the number of locally maximal solutions evolves when constraints are added  ...  We give the exponential order of the expected number of these distinguished solutions and prove it depends on the sensitivity of the allowed constraint functions only.  ...  Let L and n be integers, CSP n,L (F) is a random model for the Boolean constraint satisfaction problem with n variables and L constraints.  ... 
doi:10.46298/dmtcs.3539 fatcat:yzrnrbrrtjd2rip465urk42pxa

Functional Test Generation Using Constraint Logic Programming [chapter]

Zhihong Zeng, Maciej Ciesielski, Bruno Rouzeyre
2002 IFIP Advances in Information and Communication Technology  
The proposed SAT solver allows efficiently handling the designs with mixed word-level arithmetic operators and Boolean logic.  ...  This paper presents a novel approach to solving SAT based on Constraint Logic Programming technique.  ...  A typical design verification scenario includes random and pseudo-random directed tests, bringing the functional coverage of the design specification to a desired level.  ... 
doi:10.1007/978-0-387-35597-9_32 fatcat:uhmy4a7uxrgbnj2tq2eaiepclq

The automatic generation of functional test vectors for Rambus designs

K. D. Jones, J. P. Privitera
1996 Proceedings of the 33rd annual conference on Design automation conference - DAC '96  
We present a method for the automatic generation of test vectors for functional verification, giving the advantages of random and directed testing.  ...  We discuss our experience with this method applied to commercial designs. We show how our approach is a stepping stone towards practical formal verification.  ...  functions, and a "computed table" to hold the results of boolean function evaluations.  ... 
doi:10.1145/240518.240598 dblp:conf/dac/JonesP96 fatcat:eooxy5ibm5bhvlqecthrxljm2q

Combinatorial sharpness criterion and phase transition classification for random CSPs

Nadia Creignou, Hervé Daudé
2004 Information and Computation  
We investigate the nature of the phase transition (sharp or coarse) for random constraint satisfaction problems.  ...  Thus, we get a complete and precise classification of the nature of the threshold for symmetric Boolean CSPs.  ...  is a random graph with edge probability equivalent to t n .  ... 
doi:10.1016/j.ic.2004.01.002 fatcat:5dwowxxjyrbypjr2wlf54expta

And/or trees: A local limit point of view [article]

Nicolas Broutin, Cécile Mailler
2017 arXiv   pre-print
We prove that, under rather weak local conditions on the sequence of random trees (t_n)_n> 1, the distribution induced on Boolean functions by this procedure converges as n tends to infinity.  ...  In this latter case, we provide a relationship between the probability of a given Boolean function and its complexity.  ...  studied uniformly random k-variable Boolean functions (for large integer k).  ... 
arXiv:1510.06691v2 fatcat:zvlr7quth5etthlppgpa6hkaza

Exact Synthesis of ESOP Forms [article]

Heinz Riener and Rüdiger Ehlers and Bruno Schmitt and Giovanni De Micheli
2018 arXiv   pre-print
The approach can deal with incompletely-specified Boolean functions defined over many Boolean variables and is particularly fast if the Boolean function can be expressed with only a few product terms.  ...  Our approach finds one or more ESOP forms for a given Boolean function.  ...  For k = 9 terms, the constraint system becomes for the first time satisfiable and the corresponding ESOP form with 9 terms is returned. Random.  ... 
arXiv:1807.11103v1 fatcat:z6amgut3wvhqfpbfmmm5qzujtm

On Continuous Local BDD-Based Search for Hybrid SAT Solving [article]

Anastasios Kyrillidis, Moshe Y. Vardi, Zhiwei Zhang
2021 arXiv   pre-print
Our framework accepts all Boolean constraints that admit compact BDDs, including symmetric Boolean constraints and small-coefficient pseudo-Boolean constraints as interesting families.  ...  The algorithm is based on CLS combined with belief propagation on binary decision diagrams (BDDs).  ...  Instances in this family are composed of random pseudo-Boolean constraints.  ... 
arXiv:2012.07983v2 fatcat:zlafv7mbyjgkhoj67rnmcieogq

Improving design verifiability by early RTL coverability analysis

Kai-Hui Chang, Chia-Wei Chang, Jie-Hong Roland Jiang, Chien-Nan Jimmy Liu
2012 Tenth ACM/IEEE International Conference on Formal Methods and Models for Codesign (MEMCODE2012)  
By identifying coverability problems at early RTL design stages, design verifiability can be improved, thus reducing the effort required at the verification phase.  ...  For each sample, 25 random XOR constraints were added.  ...  Each condition is a symbolic trace that is essentially a single-output Boolean function. When the output of the function is 1, the target can be covered.  ... 
doi:10.1109/memcod.2012.6292297 dblp:conf/memocode/ChangCJL12 fatcat:57cocr6aqrbmvaiv3oftugc47i

Probabilistically Checkable Proofs and Codes

Irit Dinur
2011 Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)  
Thus such proofs can be verified by a randomized procedure that is local: it reads only a constant (!) number of bits from the proof and with high probability detects an error if one exists.  ...  The canonical example is the sat problem: given a Boolean formula, it is notoriously difficult to come up with a satisfying assignment, whereas given a proposed assignment it is trivial to plug in the  ...  . • The "majority is stablest" theorem is concerned with the noise sensitivity of Boolean functions.  ... 
doi:10.1142/9789814324359_0013 fatcat:dudwyxj3snerfjreay3bl26b4u
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