PPSZ is better than you think
D Scheder - TheoretiCS, 2024 - theoretics.episciences.org
PPSZ, for long time the fastest known algorithm for 𝑘-SAT, works by going through the
variables of the input formula in random order; each variable is then set randomly to 0 or 1 …
variables of the input formula in random order; each variable is then set randomly to 0 or 1 …
Rare-Case Hard Functions Against Various Adversaries
T Nareddy, A Mishra - arXiv preprint arXiv:2411.09597, 2024 - arxiv.org
We say that a function is rare-case hard against a given class of algorithms (the adversary) if
all algorithms in the class can compute the function only on an $ o (1) $-fraction of instances …
all algorithms in the class can compute the function only on an $ o (1) $-fraction of instances …
Local enumeration and majority lower bounds
Depth-3 circuit lower bounds and $ k $-SAT algorithms are intimately related; the state-of-the-
art $\Sigma^ k_3 $-circuit lower bound and the $ k $-SAT algorithm are based on the same …
art $\Sigma^ k_3 $-circuit lower bound and the $ k $-SAT algorithm are based on the same …
The (Coarse) Fine-Grained Structure of NP-Hard SAT and CSP Problems
V Lagerkvist, M Wahlström - ACM Transactions on Computation Theory …, 2021 - dl.acm.org
We study the fine-grained complexity of NP-complete satisfiability (SAT) problems and
constraint satisfaction problems (CSPs) in the context of the strong exponential-time …
constraint satisfaction problems (CSPs) in the context of the strong exponential-time …
Super strong ETH is true for PPSZ with small resolution width
D Scheder, N Talebanfard - 35th Computational Complexity …, 2020 - eprints.whiterose.ac.uk
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 (√{log log m}), has success probability at most …
which uses resolution of width bounded by O (√{log log m}), has success probability at most …
Isolation schemes for problems on decomposable graphs
J Nederlof, M Pilipczuk, CMF Swennenhuis… - arXiv preprint arXiv …, 2021 - arxiv.org
The Isolation Lemma of Mulmuley, Vazirani and Vazirani [Combinatorica'87] provides a self-
reduction scheme that allows one to assume that a given instance of a problem has a …
reduction scheme that allows one to assume that a given instance of a problem has a …
Faster Random -CNF Satisfiability
We describe an algorithm to solve the problem of Boolean CNF-Satisfiability when the input
formula is chosen randomly. We build upon the algorithms of Sch {\"{o}} ning 1999 and …
formula is chosen randomly. We build upon the algorithms of Sch {\"{o}} ning 1999 and …
On Extremal Properties of k-CNF: Capturing Threshold Functions
M Gurumukhani, M Künnemann, R Paturi - arXiv preprint arXiv …, 2024 - arxiv.org
We consider a basic question on the expressiveness of $ k $-CNF formulas: How well can $
k $-CNF formulas capture threshold functions? Specifically, what is the largest number of …
k $-CNF formulas capture threshold functions? Specifically, what is the largest number of …
PPSZ for General k-SAT and CSP—Making Hertli's Analysis Simpler and 3-SAT Faster
D Scheder, J Steinberger - computational complexity, 2024 - Springer
The currently fastest known algorithm for k-SAT is PPSZ, named after its inventors (Paturi et
al. in J ACM 52 (3): 337-364, 2005. http://dx. doi. org/10.1145/1066100.1066101). Analyzing …
al. in J ACM 52 (3): 337-364, 2005. http://dx. doi. org/10.1145/1066100.1066101). Analyzing …
Synthesis of asynchronous distributed systems from global specifications
J Hecking-Harbusch - 2021 - publikationen.sulb.uni-saarland.de
The synthesis problem asks whether there exists an implementation for a given formal
specification and derives such an implementation if it exists. This approach enables …
specification and derives such an implementation if it exists. This approach enables …