Solving the 3‐Satisfiability Problem Using Network‐Based Biocomputation

Abstract

The 3‐satisfiability Problem (3‐SAT) is a demanding combinatorial problem that is of central importance among the nondeterministic polynomial (NP) complete problems, with applications in circuit design, artificial intelligence, and logistics. Even with optimized algorithms, the solution space that needs to be explored grows exponentially with the increasing size of 3‐SAT instances. Thus, large 3‐SAT instances require excessive amounts of energy to solve with serial electronic computers. Network‐based biocomputation (NBC) is a parallel computation approach with drastically reduced energy consumption. NBC uses biomolecular motors to propel cytoskeletal filaments through nanofabricated networks that encode mathematical problems. By stochastically exploring possible paths through the networks, the cytoskeletal filaments find possible solutions. However, to date, no NBC algorithm for 3‐SAT has been available. Herein, an algorithm that converts 3‐SAT into an NBC‐compatible network format is reported and four small 3‐SAT instances (with up to three variables and five clauses) using the actin–myosin biomolecular motor system are experimentally solved. Because practical polynomial conversions to 3‐SAT exist for many important NP complete problems, the result opens the door to enable NBC to solve small instances of a wide range of problems.

Understanding the Role of Filamentous Actin in Food Quality: From Structure to Application

“…Over the past few decades, actin filaments and their associated motor systems have been explored for nanotechnology applications, including nanotransportation, nanocommunication, diagnostics, biocomputation, miniaturized sensor systems and lab-on-a-chip devices, among others. We hope that actin, as a great source of one of the most plentiful eukaryotic proteins, can be applied more widely in basic research in human health and diseases.…”

Nanolithographic Fabrication Technologies for Network-Based Biocomputation Devices

“…In the field of network-based biocomputation, it has been proven that wafer-level NBC devices can successfully encode classical non-deterministic polynomial-time complete (“NP-complete”) problems, such as the exact-cover (ExCov) problem [ 13 ] and the satisfiability problem for three literals (3-SAT) [ 6 ], with details of the fabrication workflow touched on only briefly. In this paper, we report on a convergent optimized fabrication technology for NBC devices on the wafer level, illustrating the operation of a biocomputation network that encodes the subset-sum problem (SSP).…”

“…In the case of NBC, motile physical objects can be represented by self-propelled microorganisms [ 3 ] or motile (yet passively guided) cytoskeletal filaments driven by localized molecular motors [ 4 ]. For different types of agents and molecular motors [ 3 , 4 , 5 , 6 , 7 , 8 ], there are various run modes and scaling parameters [ 9 ].…”

Improved longevity of actomyosin in vitro motility assays for sustainable lab-on-a-chip applications

“…Such systems allow unprecedented miniaturization and the independence of bulky and expensive accessory equipment such as high-pressure pumps required to drive nano uidic transport. Network based biocomputation [34][35][36][37] , where exploration of large, nanofabricated networks by myosin propelled actin laments solves complex mathematical problems, is a related application where prolonged motor function is important. The reason is that effective computation requires a very large number of exploring actin laments.…”