| Autor: |
Grosshans, Nathan, Mckenzie, Pierre, Segoufin, Luc |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Logical Methods in Computer Science, Volume 18, Issue 3 (August 2, 2022) lmcs:7110 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.46298/lmcs-18(3:14)2022 |
| Popis: |
The program-over-monoid model of computation originates with Barrington's proof that the model captures the complexity class $\mathsf{NC^1}$. Here we make progress in understanding the subtleties of the model. First, we identify a new tameness condition on a class of monoids that entails a natural characterization of the regular languages recognizable by programs over monoids from the class. Second, we prove that the class known as $\mathbf{DA}$ satisfies tameness and hence that the regular languages recognized by programs over monoids in $\mathbf{DA}$ are precisely those recognizable in the classical sense by morphisms from $\mathbf{QDA}$. Third, we show by contrast that the well studied class of monoids called $\mathbf{J}$ is not tame. Finally, we exhibit a program-length-based hierarchy within the class of languages recognized by programs over monoids from $\mathbf{DA}$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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