Amoeba-inspired SAT Solver

†Flucto-order Functions Research Team, RIKEN Advanced Science Institute,‡Tokyo Tech-RIKEN International School, Tokyo Institute of Technology,2-1, Hirosawa, Wako, Saitama 351-0198, Japan£Photonic Network Research Institute, National Institute of Information and Communications Technology,4-2-1 Nukui-kita, Koganei, Tokyo 184-8795, Japan§Graduate School of Engineering, The University of Tokyo,2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan¶Interdisciplinary Graduate School of Medical and Engineering, University of Yamanashi,Kofu 400-8511, JapanEmail: masashi.aono@riken.jpAbstract—We propose a biologically-inspired comput-ing algorithm called “AmoebaSAT” for solving an NP-completecombinatorialoptimizationproblem,theBooleansatisfiability problem (SAT). AmoebaSAT is a hybrid oftwo dynamics; chaotic oscillatory dynamics for exploringthe state space are combined with spatiotemporal controldynamics for bouncing back logically-false state transi-tions. For the former, we employ the logistic map as a unitfor generating chaotic fluctuation. The control principle ofthe latter that we call “bounceback control” is designed tostabilize a state only when it represents a solution, i.e., asatisfiable assignment. We show that, for some benchmarkprobleminstances,AmoebaSATfindsasolutionfasterthana well-known algorithm called “WalkSAT”, which is con-sidered to be one of the fastest algorithms.1. IntroductionThere has been growing interest in biologically-inspiredalgorithms for solving computationally demanding prob-lems in a fashion similar to search dynamics of variousbiological systems such as neural networks, evolutionaryprocesses, ants, and swarms [1]. AmoebaSAT extracts theessence of spatiotemporal oscillatory dynamics of a single-celled amoeboid organism, the true slime mold Physarumpolycephalum, which is capable of searching for a solu-tion to some optimization problems [2]. When placed un-der our previously studied spatiotemporal control whichapplies aversive light stimuli locally and dynamically de-pending on the shape of the organism, the organism ex-hibits chaotic oscillatory dynamics and finds a solution tothe traveling salesman problem by changing its shape intothe optimal one for which the area of the body is maxi-mized and the risk of being illuminated is minimized [3].Inspiredbythisscheme,wedefineAmoebaSATasahybridof chaotic oscillatory dynamics and spatiotemporal controldynamics.The SAT is the problem of determining if a givenBoolean formula of N variables x