Optimal L-Systems for Stochastic L-system Inference Problems
<|reference_start|>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 maximizes the likelihood of producing a given sequence of words through a singular derivation. 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 sophisticated optimization techniques, such as interior point methods, ensuring production of a stochastically optimal stochastic L-system suitable for generating the given sequence. This allows for the use of using stochastic L-systems as model for machine learning using only positive data for training.<|reference_end|>
@article{lotfi2024optimal,
    title={Optimal L-Systems for Stochastic L-system Inference Problems},
    author={Ali Lotfi and Ian McQuillan},
    journal={arXiv preprint arXiv:2409.02259},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.02259},
    primaryClass={cs.LG cs.CL cs.CV cs.DS cs.FL}
}