A Study of Parallel Continuous Local Search
Quick Answer
This study explores parallel Continuous Local Search (CLS) for solving Boolean satisfiability problems with symmetric pseudo-Boolean constraints.
Quick Take
This study explores parallel Continuous Local Search (CLS) for solving Boolean satisfiability problems with symmetric pseudo-Boolean constraints. Key findings include that redundant constraints can slow convergence, CLS can effectively serve as a sub-solver in hybrid settings, and local search quickly stabilizes solution quality due to diminishing returns from additional solver steps. These insights are crucial for optimizing SAT problems on modern hardware.
Key Points
- Redundant constraints can inhibit convergence in CLS.
- CLS shows potential as a sub-solver in hybridized SAT settings.
- Local search converges rapidly to a stable solution quality distribution.
- Saddle-dense objectives lead to diminishing returns in solver steps.
- Findings enhance practical applications of CLS on modern accelerators.
Article Excerpt
From source RSS / original summaryarXiv:2606. 06656v1 Announce Type: new Abstract: We study parallel Continuous Local Search (CLS) as a solution approach for Boolean satisfiability problems with symmetric pseudo-Boolean (PB) constraints. Here, the $n$-variable PB-satisfiability problem is relaxed to a continuous optimisation problem with a differentiable objective function on an $n$-dimensional hypercube. For satisfiable instances, the global minimisers of this optimisation problem correspond to satisfying assignments of the SAT problem at hand.
We present several novel findings via empirical experiments: (i) redundant constraints can inhibit rather than accelerate convergence; (ii) CLS shows promise as a sub-solver in hybridised settings, quickly completing partial assignments; and (iii) local search rapidly converges to a stable distribution of solution quality (i. e. , degree of satisfaction), due to saddle-dense objectives where additional solver steps yield diminishing returns.
Our findings inform practical uses of CLS for SAT on modern accelerator hardware.
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