# Evidence for Long-Tails in SLS Algorithms

arXiv: https://arxiv.org/abs/2107.00378 · HTML: https://mlsanity.com/paper/2107.00378/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 38 references that are in the map.
- First posted on arXiv 1 Jul 2021.

## Builds on (most cited first, 4 of 4)

- [Runtime Distributions and Criteria for Restarts](https://mlsanity.com/paper/1709.10405/) (2017)
- [On the Effect of Learned Clauses on Stochastic Local Search](https://mlsanity.com/paper/2005.04022/) (2020)
- [Evaluating Las Vegas Algorithms - Pitfalls and Remedies](https://mlsanity.com/paper/1301.7383/) (2013)
- [Algorithm Portfolio Design: Theory vs. Practice](https://mlsanity.com/paper/1302.1541/) (2013)

## Built on by (most cited first, 2 of 2)

- [Too much information: why CDCL solvers need to forget learned clauses](https://mlsanity.com/paper/2202.01030/) (2022)
- [Towards an Understanding of Long-Tailed Runtimes of SLS Algorithms](https://mlsanity.com/paper/2210.13159/) (2022)

## Abstract (arXiv)

Stochastic local search (SLS) is a successful paradigm for solving the satisfiability problem of propositional logic. A recent development in this area involves solving not the original instance, but a modified, yet logically equivalent one. Empirically, this technique was found to be promising as it improves the performance of state-of-the-art SLS solvers. Currently, there is only a shallow understanding of how this modification technique affects the runtimes of SLS solvers. Thus, we model this modification process and conduct an empirical analysis of the hardness of logically equivalent formulas. Our results are twofold. First, if the modification process is treated as a random process, a lognormal distribution perfectly characterizes the hardness; implying that the hardness is long-tailed. This means that the modification technique can be further improved by implementing an additional restart mechanism. Thus, as a second contribution, we theoretically prove that all algorithms exhibiting this long-tail property can be further improved by restarts. Consequently, all SAT solvers employing this modification technique can be enhanced.