Minimal Macro-Based Rewritings of Formal Languages: Theory and Applications in Ontology Engineering (and beyond)

In this paper, we introduce the problem of rewriting finite formal languages using syntactic macros such that the rewriting is minimal in size. We present polynomial-time algorithms to solve variants of this problem and show their correctness. To demonstrate the practical relevance of the proposed problems and the feasibility and effectiveness of our algorithms in practice, we apply these to biomedical ontologies authored in OWL. We find that such rewritings can significantly reduce the size of ontologies by capturing repeated expressions with macros. In addition to offering valuable assistance in enhancing ontology quality and comprehension, the presented approach introduces a systematic way of analysing and evaluating features of rewriting systems (including syntactic macros, templates, or other forms of rewriting rules) in terms of their influence on computational problems.