Regular languages form a dense, incomplete ultrametric subspace of all formal languages, and guarded fixed-point iteration produces finite automata with certified agreement up to a specified word length.
Guarded Language Operators as Contractions in a Length-Based Ultrametric Space.Mathematics2026,14, 1644
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Ultrametric Convergence of Guarded Automata and Applications to Structural Input Validation
Regular languages form a dense, incomplete ultrametric subspace of all formal languages, and guarded fixed-point iteration produces finite automata with certified agreement up to a specified word length.