Compositional Object Synthesis in Game of Life Cellular Automata Using SAT Solver

Abstract

Conway’s Game of Life is a two-dimensional cellular automata known for the emergence of objects (i.e., patterns with special properties) from simple transition rules. So far, various interesting objects named still-life, oscillator, and spaceship have been discovered, and many methods to systematically search for such objects have been proposed. Most existing methods for finding objects have comprehensively search all patterns. However, attempting to obtain a large object in this way may cause a state explosion. To tackle this problem and enhance scalability, in this study, we propose a method to generate objects by synthesizing some existing objects. The basic idea is to arrange multiple pieces of existing objects and compose them by complementing the appropriate patterns. The problem of finding complementary patterns is reduced to the propositional satisfiability problem and solved using SAT solver. Our method can reduce the object generation time compared to the case where a large object is generated from the beginning. We also demonstrate the usefulness of our proposed method with an implementation for automatic object generation.