There is an increasing level of interest in open-endedness in the recent literature of Artificial Life and Artificial Intelligence. We previously proposed the cardinality leap of possibility spaces as a promising mechanism to facilitate open-endedness in artificial evolutionary systems, and demonstrated its effectiveness using Hash Chemistry, an artificial chemistry model that used a hash function as a universal fitness evaluator. However, the spatial nature of Hash Chemistry came with extensive computational costs involved in its simulation, and the particle density limit imposed to prevent explosion of computational costs prevented unbounded growth in complexity of higher-order entities. To address these limitations, here we propose a simpler non-spatial variant of Hash Chemistry in which spatial proximity of particles are represented explicitly in the form of multisets. This model modification achieved a significant reduction of computational costs in simulating the model. Results of numerical simulations showed much more significant unbounded growth in both maximal and average sizes of replicating higher-order entities than the original model, demonstrating the effectiveness of this non-spatial model as a minimalistic example of open-ended evolutionary systems.

翻译：近年来，人工生命与人工智能领域的文献对开放性的关注日益增加。我们先前提出将可能性空间的数量级跃迁作为促进人工进化系统开放性的潜在机制，并通过哈希化学（一种使用哈希函数作为通用适应度评估器的人工化学模型）验证了其有效性。然而，哈希化学的空间特性导致其模拟过程产生巨大计算成本，且为防止计算爆炸而设的粒子密度上限阻碍了高阶实体复杂度的无界增长。为解决这些局限，本文提出一种更简洁的非空间变体哈希化学模型——在该模型中，粒子的空间邻近性以多重集形式显式表征。这种模型改进显著降低了模拟计算成本。数值仿真结果显示，相较于原始模型，复制型高阶实体的最大尺寸与平均尺寸均展现出更显著的无界增长，验证了该非空间模型作为极简开放式进化系统的有效性。