Summary
A dual bordered OS system is a triple (∑, P, S) where ∑ is a finite alphabet, S a finite subset of ∑*, the set of axioms, and P a finite set of rules of the form a→a × a, where a ε ∑ and x ε ∑ *. Using well-quasi-order theory, we show that the regularity problem for such systems is decidable. Whether such a system generates a regular language essentially only depends on the set of rules but not on the axioms.
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Bucher, W. A regularity test for dual bordered OS systems. Acta Informatica 23, 245–253 (1986). https://doi.org/10.1007/BF00289112
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DOI: https://doi.org/10.1007/BF00289112