# 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} }

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

- Computer ScienceICALP
- 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.

Results on a Super Strong Exponential Time Hypothesis

- MathematicsAAAI
- 2020

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.

Super Strong ETH is False for Random k-SAT

- Computer ScienceArXiv
- 2018

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

- MathematicsSAT
- 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 ScienceComputational 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

- Computer ScienceSIGA
- 2018

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

- MathematicsSTOC
- 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, MathematicsSAT
- 2017

Itsykson and Sokolov have proved first exponential lower bounds for \(\mathrm {DPLL}(\oplus )\) algorithms on unsatisfiable formulas.

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