Abstract
We propose a new, logical, approach to the decidability prob- lem for the Straubing and Brzozowski hierarchies based on the preser- vation theorems from model theory, on a theorem of Higman, and on the Rabin tree theorem. In this way, we get purely logical, short proofs for some known facts on decidability, which might be of methodological interest.
Our approach is also applicable to some other similar situations, say to “words” over dense orderings which is relevant to the continuous time and hybrid systems.
Partly supported by the Alexander von Humboldt Foundation, by a grant of the Russian Ministry of Education and by RFBR Grant 00-01-00810.
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Selivanov, V.L. (2001). A Logical Approach to Decidability of Hierarchies of Regular Star—Free Languages. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_47
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DOI: https://doi.org/10.1007/3-540-44693-1_47
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