# Tighter Hard Instances for PPSZ

@article{Pudlk2017TighterHI,
title={Tighter Hard Instances for PPSZ},
author={Pavel Pudl{\'a}k and Dominik Scheder and Navid Talebanfard},
journal={ArXiv},
year={2017},
volume={abs/1611.01291}
}
• Published 4 November 2016
• Computer Science, Mathematics
• ArXiv
We construct uniquely satisfiable k-CNF formulas that are hard for the PPSZ algorithm, the currently best known algorithm solving k-SAT. This algorithm tries to generate a satisfying assignment by picking a random variable at a time and attempting to derive its value using some inference heuristic and otherwise assigning a random value. The "weak PPSZ" checks all subformulas of a given size to derive a value and the "strong PPSZ" runs resolution with width bounded by some given function…
10 Citations
Faster Random k-CNF Satisfiability
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ICALP
• 2020
An algorithm to solve the problem of Boolean CNF-Satisfiability when the input formula is chosen randomly by counting how many clauses are satisfied by each randomly sampled assignment, and only search in the neighborhoods of assignments with abnormally many satisfied clauses is described.
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• Mathematics
AAAI
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A randomized algorithm is given which refutes the Super-Strong ETH for the case of random k-SAT and planted k- SAT for any clause-to-variable ratio, and shows the time complexities of Unique k- sAT and k-sAT are very tightly related.
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A randomized algorithm which refutes the Super-Strong ETH for the case of random $k-SAT, for any clause-to-variable ratio, using the PPZ algorithm of Paturi, Pudlak, and Zane (1998). On Super Strong ETH • Mathematics SAT • 2019 A randomized algorithm is given which refutes the Super-Strong ETH for the case of random k-SAT and planted k- SAT for any clause-to-variable ratio, and it turns out that a well-known algorithm from the literature on SAT algorithms does the job. Super strong ETH is true for PPSZ with small resolution width • Mathematics, Computer Science Computational Complexity Conference • 2020 We construct k-CNFs with m variables on which the strong version of PPSZ k-SAT algorithm, which uses resolution of width bounded by O([MATH HERE]), has success probability at most 2-(1-(1+∈)2/k)m for Some Open Problems in Fine-Grained Complexity Fine-grained complexity studies problems that are "hard" in the following sense. Consider a computational problem for which existing techniques easily give an algorithm running in a(n) time for Super Strong ETH is True for PPSZ • Mathematics, Computer Science • 2020 We construct k-CNFs with m variables on which the strong version of PPSZ kSAT algorithm, which uses bounded width resolution, has success probability at most 2−(1−(1+ )2/k)m for every > 0. Previously Faster k-SAT algorithms using biased-PPSZ • Mathematics STOC • 2019 A biased version of the PPSZ algorithm is introduced using which an improvement over PPSz is obtained for every k≥ 3 and for Unique 3-SAT the current bound is improved from 1.308n to 1.307n. Hard Satisfiable Formulas for Splittings by Linear Combinations • Computer Science, Mathematics SAT • 2017 Itsykson and Sokolov have proved first exponential lower bounds for $$\mathrm {DPLL}(\oplus )$$ algorithms on unsatisfiable formulas. ## References SHOWING 1-10 OF 20 REFERENCES An improved exponential-time algorithm for k-SAT • Computer Science JACM • 2005 A simple new randomized algorithm, called ResolveSat, for finding satisfying assignments of Boolean formulas in conjunctive normal form, which is the fastest known probabilistic algorithm for k-CNF satisfiability and proves a lower bound on the number of codewords of a code defined by a <i>k</i>-C NF. Exponential Lower Bounds for the PPSZ k-SAT Algorithm • Mathematics, Computer Science SODA • 2013 This paper constructs hard instances for PPSZ, an elegant randomized algorithm for k-SAT that proves that its expected running time on k-CNF formulas with n variables is at most 2(1−ek)n, where ek e Ω(1/k). 3-SAT Faster and Simpler - Unique-SAT Bounds for PPSZ Hold in General The PPSZ algorithm by Paturi, Pudlak, Saks, and Zane is shown to be the fastest known algorithm for Unique$k\$-SAT, where the input formula does not have more than one satisfying assignment, and it is shown that this is also the case for k=3,4.
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