Optimal L-Systems for Stochastic L-system Inference Problems

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.