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Research questionWhen does unique factorization under a fixed finite-monoid observation admit a finite-state canonical presentation?Unique exact factorization can coexist with infinitely many valid prime-return rules, so a finite quotient alone does not guarantee a finite canonical presentation. The central difficulty is determining when those rules can be represented by finite residual controllers.
Research Paper
Latest papersRecent research connected to this question, newest first.Relative Prime Factorization and Finite-State Presentations under Fixed Finite-Monoid ObservationThe source gives a 36-element finite-quotient counterexample, lifts the presentation defect to a nonregular context-free language, and studies prime-target left-division determinism as a sufficient condition for stronger factorization and presentation behavior. It also reports positive-data learning results for canonical presentations under the fixed morphism.research paper · Sep 3, 2026
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