Decidability and closure properties for rule-synchronized music grammar systems

Determine the decidability of standard decision problems and characterize closure properties under common language operations for n-generative rule-synchronized music grammar systems whose components are scattered context grammars without erasing rules.

Background

The paper introduces n-generative rule-synchronized music grammar systems, where each component is a scattered context grammar (without erasing rules), to orchestrate multi-instrument musical compositions. Each component corresponds to an instrument, and a global synchronization set coordinates parallel rule applications.

While the paper focuses on modeling and illustrative orchestration examples, it explicitly points to foundational formal-language-theoretic questions as open problem areas, calling for the paper of decidability and closure properties for these systems.