Stochastic L-system inference from multiple string sequence inputs

Lindenmayer systems (L-systems) are a grammar system that consists of string rewriting rules. The rules replace every symbol in a string in parallel with a successor to produce the next string, and this procedure iterates. In a stochastic context-free L-system (S0L-system), every symbol may have one or more rewriting rule, each with an associated probability of selection. Properly constructed rewriting rules have been found to be useful for modeling and simulating some natural and human engineered processes where each derived string describes a step in the simulation. Typically, processes are modeled by experts who meticulously construct the rules based on measurements or domain knowledge of the process. This paper presents an automated approach to finding stochastic L-systems, given a set of string sequences as input. The implemented tool is called the Plant Model Inference Tool for S0L-systems or PMIT-S0L. PMIT-S0L is evaluated using 960 procedurally generated S0L-systems in a test suite, which are each used to generate input strings, and PMIT-S0L is then used to infer the system from only the sequences. The evaluation shows that PMIT-S0L infers S0L-systems with up to 9 rewriting rules each in under 12 hours. Additionally, it is found that 3 sequences of strings are sufficient to find the correct original rewriting rules in 100 % of the cases in the test suite, and 6 sequences of strings reduce the difference in the associated probabilities to approximately 1 % or less.