Advanced Intelligent Systems (Dec 2022)

Solving the 3‐Satisfiability Problem Using Network‐Based Biocomputation

  • Jingyuan Zhu,
  • Aseem Salhotra,
  • Christoph Robert Meinecke,
  • Pradheebha Surendiran,
  • Roman Lyttleton,
  • Danny Reuter,
  • Hillel Kugler,
  • Stefan Diez,
  • Alf Månsson,
  • Heiner Linke,
  • Till Korten

DOI
https://doi.org/10.1002/aisy.202200202
Journal volume & issue
Vol. 4, no. 12
pp. n/a – n/a

Abstract

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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.

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