Markov Senior: Learning Markov Junior Grammars to Generate User-specified Content

Markov Junior is a probabilistic programming language used for procedural content generation across various domains. However, its reliance on manually crafted and tuned probabilistic rule sets, also called grammars, presents a significant bottleneck, diverging from approaches that allow rule learning from examples. In this paper, we propose a novel solution to this challenge by introducing a genetic programming-based optimization framework for learning hierarchical rule sets automatically. Our proposed method 'Markov Senior' focuses on extracting positional and distance relations from single input samples to construct probabilistic rules to be used by Markov Junior. Using a Kullback-Leibler divergence-based fitness measure, we search for grammars to generate content that is coherent with the given sample. To enhance scalability, we introduce a divide-and-conquer strategy that enables the efficient generation of large-scale content We validate our approach through experiments in generating image-based content and Super Mario levels, demonstrating its flexibility and effectiveness. In this way, 'Markov Senior' allows for the wider application of Markov Junior for tasks in which an example may be available, but the design of a generative rule set is infeasible.