Compiling Rewrite Rules to Finite-State Transducers with the Worsening Trick

Abstract: Finite-state transducers (FSTs) are essential for modeling string rewriting in computational linguistics and NLP, particularly for phonological and morphological rewrite rules. Compiling general rewrite rules of the form $A \to B / L \, _ \, R$, where $A$, $B$, $L$, and $R$ are arbitrary regular languages, is complex due to overlapping matches and context constraints. Traditional methods, such as those by Kaplan and Kay or Karttunen, rely on intricate transducer compositions with auxiliary markers. This paper presents a compact compilation scheme based on the "worsening trick'': generate all legal rewrite candidates, then filter candidates that are worse than another candidate for the same input. Implemented as the built-in rewrite compiler in PyFoma, the construction supports multiple contexts, arbitrary transductions, markup, directed rewriting, weights, and parallel rewriting. The resulting formulas are short and uniform, and where semantics coincide, they reproduce the same rule transducers as earlier approaches while remaining easier to extend. The implementation has been validated against foma on both a substantial collection of rewrite grammars and an automated regression suite covering the major rewrite modalities, with the resulting transducers matching exactly apart from state numbering.