Computing in the fractal cloud: modular generic solvers for SAT and Q-SAT variants

TL;DR

This paper introduces a modular, fractal-based computing approach using signal machines and Map/Reduce to efficiently solve SAT and Q-SAT variants within bounded space and time, emphasizing flexibility and generality.

Contribution

It presents a novel, modular framework for constructing generic machines that solve SAT variants using fractal parallelization and signal machines, extending previous geometrical computation methods.

Findings

Efficient solution of Q-SAT in bounded space and time.

Modular construction allows easy adaptation to SAT variants.

Fractal parallelization enhances computational capabilities.

Abstract

Abstract geometrical computation can solve hard combinatorial problems efficiently: we showed previously how Q-SAT can be solved in bounded space and time using instance-specific signal machines and fractal parallelization. In this article, we propose an approach for constructing a particular generic machine for the same task. This machine deploies the Map/Reduce paradigm over a fractal structure. Moreover our approach is modular: the machine is constructed by combining modules. In this manner, we can easily create generic machines for solving satifiability variants, such as SAT, #SAT, MAX-SAT.