提出最优随机L系统构造方法，用正样本训练生成指定字符串序列。
Optimal L-Systems for Stochastic L-system Inference Problems
- 基于概率最大化原则构建随机L系统，支持单次或多次推导。
- 算法结合内点法优化，使生成目标序列的概率达到理论上限。
- 适用于仅用正例训练的机器学习场景，无需负样本。
本文提出两个新定理，解决随机林登迈尔系统（L-system）推断中的两个开放问题，重点在于构造一个能生成给定字符串序列的最优随机L系统。第一个定理描述了一种方法，可构造出在单次推导中产生指定字符串序列概率最高的随机L系统（尽管多个推导可能生成相同序列）。第二个定理则确定了在存在多种可能推导时，使目标序列生成概率最大的随机L系统。基于此，我们设计了一种从给定序列中推断最优随机L系统的算法，该算法采用内点法等先进优化技术，确保所构造系统在生成目标序列上的概率最大化（允许存在多条推导路径）。这使得随机L系统可作为仅需正样本进行训练的机器学习模型使用。
原文摘要 · Abstract (English)
This paper presents two novel theorems that address two open problems in stochastic Lindenmayer-system (L-system) inference, specifically focusing on the construction of an optimal stochastic L-system capable of generating a given sequence of strings. The first theorem delineates a method for crafting a stochastic L-system that has the maximum probability of a derivation producing a given sequence of words through a single derivation (noting that multiple derivations may generate the same sequence). Furthermore, the second theorem determines the stochastic L-systems with the highest probability of producing a given sequence of words with multiple possible derivations. From these, we introduce an algorithm to infer an optimal stochastic L-system from a given sequence. This algorithm incorporates advanced optimization techniques, such as interior point methods, to ensure the creation of a stochastic L-system that maximizes the probability of generating the given sequence (allowing for multiple derivations). This allows for the use of stochastic L-systems as a model for machine learning using only positive data for training.
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